Leveling bathroom floor

Background info:

I'm laying ceramic tile in my bathroom (12"x12" tile). There's already an inch of sub floor (with vinyl in there now, which is solid and not pulling up at all) and I'm adding 1/4" backer board before laying the tile. The bathroom is long and narrow - about 3' x 12', and the joists (2x10's) run length-wise down the room. They're 16" OC.

Two joists can be completely seen down the length of the room, while the third can be seen in front of the toilet and vanity, but is covered by a wall for the linen closet. I have full access to them from the unfinished basement below.

See the attached image for the layout.

The problem:

The middle joist is between a 1/4" and 3/8" higher than the other two (which appear level with each other from the basement). So while level going length wise, it humps pretty bad in the middle of the room.

That obviously won't fly for the tile.

Solutions?

Since I can't uncover the joists on each side of the high one (because of the linen closet), I can't remove the sub flooring, shave the joist, and replace it easily. So, the two options I thought of, either of which may work or they both might be complete crap:

1. Remove something like 4" of floor on each side of the middle joist, shave it down, and replace the flooring. Since I won't be able to sit the new sub floor on the adjoining joists, I could place 2x10's perpendicular between the middle truss and each side truss for the flooring to sit on. I have to think placing them every 16" going the length of the bathroom would suffice?
2. Use one of those oscillating tools (like this) to just trim the 1/4" I need from the joist in the basement. Would this even be possible to do while leaving the floor in place? There can't be much if any weight on that joist other than the flooring? This idea seems a bit crazier, but it'd be easier (I think).

I hope that's enough info. Would either of these ideas work? Any other suggestion?

I'd rather do this right - however that may be - rather than using a hack. That auto-leveling liquid stuff that a friend suggested seems cheap, plus it'd raise the toilet, which would mean either extenders or raising the flange.

Thanks for the help guys!

The joists should have a crown up if the outside joists are sagging or have been put in upside down, You may want to address them. Often these kind of things show up in older houses. I like your idea of trimming the joist at the walls so it would settle down, but you will have up to 5 nails thru the rimm joist into this joist. A sawsall would be the tool of choice. Check the total height of the joists, If they are all the same size and you have one that has an extra high crown, it may be easier to just to cut the joist and sister on a new one.

To do this right you can not just install tile board over old linolum. If the floors 1" think then that means there's also a layer of 1/4 louon on that floor which is aslo not a sutable underlayment for tile. Trying to adjust that floor joist from below is most likly just not going to work. There's just no way to get a level cut with a sawsall in that position.
An ossilating tool will not cut through the nails and would take forever to make a cut that long.
The best thing to do would be to cut out the whole flooring using a toe kick saw for the outside edges an ossilating saw for the end cuts and a ciruler saw to make cuts between the joist.
Pull a string to check the floor joist cut if there to high and sister 2X6's if there to low. Use Advantec subflooring held in place with constrution adhesive on the joist and screw it down with 2-1/2" ceramic deck screws. Add a layer of underlayment at least 3/8 thick or A/C subfloor rated plywood making sure not to have the seams line up with the seams below. We use a pneumatic narrow crown staple gun for this job becaue it will need to be fastened every 4" on the edges and every 6 to 8" in the field, with the staple gun I can do a 4 X 8 section in about 2 min.
Then you apply the tile board setting in thin set spread out with a 3/8 trowl.
Tape the seams with tile board tape and thin set.
If a customer asked me to do it the way your suggesting I would flat out refuse to do the job because I know it would not hold up, and guess who would forget that they told me to do it that way when someone asked how come there tiles cracking.

joecaption: You're right - there's 1/2" of subfloor and 1/2" of louon to bring it flush with the hardwood in the rest of the house. Never saw that toe kick saw before - pretty neat! Thinking I'll just tear everything up, fix the hight joist, and put down new subfloor for the tile. Thanks!

So I tore out the floor down to the joists to level it all out and get rid of the louon.

Are two layers of 1/2" (with adhesive & screws between) good enough for a subfloor, or should I do 3/4" and 1/4"?

Thanks!

Go with 3/4 to start, You can get 1 inch

Do you mean use 1/4" on top of 3/4", or do they actually make a single 1" thick subfloor piece?

we use it for stair treads it is not tongue and grove. All lumber yards here carry it. 4x8 sheets

It need to be 3/4 Advantec that's T&G or it will flex at the joints, it needs to have constrution adhesive on the tops of the joist and it's better to screw it down not nail it. We use an impact screw gun for this with ceramic coated decking screws, then at least 3/8 (1/2 would be better) A/C subfloor rated plywood. Subfloor rated means there's no voids in the core and all holes have been pluged or filled on the surface, and it will have exterier rated glue.
This must be laid so the seams do not line up with the seams below and nailed or stapled every 4" on the outside edges and every 6 to 8" in the field.
We use a pneumaic narrow crown staple gun with 1-1/4 staples for this one. I can staple a whole sheet in about 1 min.
1/4 wood of any kind is not exceptable when doing tile!!!
Now you use a 3/8 spaced tile to spread out a layer of thin set and set the 1/4 tile board on top of that. Never use the premixed thin set, buy it in the bag and mix your own.
Attach the tile board using tile board screws. Once again that Ryobi impact screw gun comes in handy. I mention the Ryobi brand because it cost 1/2 as much as the others, the batterys also cost about 1/2 as much and I've had very good luck with them. A cordless drill will be use less on this job.
I like to let that sit over night then come back the next day and seal the seams with tile board tape and thin set and start setting the tile.
It's best to start in the middle of the room in most cases so the tiles come out even on the cut end pieces. You can buy spacers in 4 differant thickness to help keep the tiles lined up. The narrower the grout line the easyer the floor will be to clean.
Let that sit over night and come back the next day and grout. Never leave any extra grout on the tile, wipe it off with a damp sponge.
Once that's dry (read the bottle of sealer for time to wait) the grout will need to be sealed.