Hello Racerboy and Welcome to the Community:
The lack of vents will certainly make some drains gurgle but it would never cause tha blockage in the sewer.
There may be a maple tree that has found a leak in the sewer and is going into the sewer for the water and natural fertilizer. They will stop a drain in a hurry and, when you snake the drain, you may not be getting all of the blockage back. Some of it goes on into the city sewer.
Another notorious blocker is bermuda grass. It has a root system 3' deep or more and will invade a sewer for water; rapidly growing roots into the sewer to pick up water and food.
One easy fix for the sewer blockage is to get a bag of the water softener salt pellets and flush a cup of them every week. They are large enough to become tangled in any roots and will lay there and feed salt to the roots, which keeps them killed.
If your sewer is vitrified clay pipe it is good for a lifetime or two; it just gets cracks in the joints and allows roots in. If it is Orangeburg pipe (which is made of roofing felt and tar in layers) prepare to have it replaced. It can collapse completely.
There is a new innovation where they dig up both ends of the sewer and run a cable through it, attach a cutter head and new pipe to it and pull the new pipe through the old without distrubing the surface, driveways, flowerbeds and such.
Yes, more vents would help the water to drain quicker but I don't think that is your problem. If you can open a small place in the wall behind the bath sink, take the trap and exposed pipe off, remove the ell inside the wall and replace it with a tee. There is a mechanical vent that is illegal anywhere except in trailers, that can be screwed into the top of the tee. It is easier than trying to run a new vent pipe and cutting into the house drain while costing quite a bit less. You may have to go to a Mobile Home parts place to get one of those vents but one in each bathroom would relieve some of your problems.