You are on the exact same page as what I'd suggest

I'd cut the side wall ~ 2' up all around and remove the wall part of the liner. Then I'd fold the liner back on itself to expose 1/2 the floor (some of the sand will stick to the bottom of the liner, just sweep it off). Retrowel that 1/2 then recover the freshly troweled sand with the liner and peel back the other 1/2 and do the same.

When you pull out the old liner, you'll have to touch up a fair amount of the floor and cove. However, most of the work has already been done, so it should be a lot less work to get the bottom ready for the new liner.

Also, when you expose the walls, you can check to see if they need any attention, and take care of anything well before you are ready to drop the liner.

If, as the bottom is being retroweled, you need any tips & tricks on troweling sand for a pool, let me know and I'll try to explain how I've always done sand bottoms.

Please make sure you get replacement sand that is OK for pool bottoms (the 50 lb bags of kid's sandbox sand isn't - and you can get a better price at the local 'Contractor's Supply'.)

Well wishes for a successful liner drop and great pool season!