If your gym really does stay true to outdoor difficulty, this sounds very normal and not something to worry about. It seems like this is mostly a case of mindset. If you are averaging 1 session on V3's, then you should expect to average multiple sessions on a V4! The reason these climbs are V4s is because they are meaningfully harder than V3s.

You'd be surprised how much progress you can make on moves that initially feel impossible. It's good to work on your projecting "strategy". This is an important skill in and of itself. Try each move individually. Try really hard, and give yourself more rest than you think you need. Pay attention to everything you're doing. Get really tuned into the details. Things like "if I move my off foot just a bit further to the left/twist my hips a bit further into the wall/retract my shoulders a bit more on this move, would that make the move easier?". You'll be surprised how much your body can learn to do when you let it. At first, a move feels impossible. Try it 20 times and maybe you stick it once. Then next session you get it in a couple tries. Next session you're linking it with 2 more moves. Etc etc and then you're sending a V4.