I use large amounts of both products. Poly is good for flooring but not for exterior door applications. Spar varnish is excellent for furniture and exterior doors.
I would do a deep sanding on the door (200 grit). Follow with a thorough scrub down with a fibre scrubbie (green pad) that is saturated with acetone. (use chemical gloves and do not pour the acetone on the wood directly) This removes more of the original finish and any remaining oils. Finish sand with 300 grit or finer. Rub down with tack cloth to remove remaining dust.
DO NOT shake the spar varnish. This introduces bubbles into the varnish which can transmit to the door surface. Use a dense foam brush to trail the varnish onto the surface being careful not to move so fast that it causes bubbles via cavitation. Work the length of the wet area to help remove any brush marks. Apply one light coat. Allow a day to dry sand >300 grit, tack cloth, then next coat.
I apply three coats. Here is a hint to get the varnish to lay down even better ... Heat a pot of water to tiny bubbles but NOT boiling. Just pop open the spar varnish a bit and set the can in the pot of water off the stove for a few minutes. This will heat the varnish and it will become even more fluid. Adjust your brushing technique accordingly and keep the coats light each time.
BTW ... Am installing a new walnut entry door with a sidelight today. It is unfinished so this project will be soup to nuts. Will try to take pics.
This is how it might look when done ...
