I think I know what you're saying, but I think you just haven't developed the muscles yet for the more standard "compact" riding form.
Check out Greg LeMond and his position on the bike, I think this is how you are riding. Note like others have said that your bikes top tube is too short for this style. This is the classic "French fit".
You are bodging your position with "the seat between thighs". If you get a bike with a longer top tube versus seattube you can ride "stretched out". You should search out an old LeMond bike.
Yes I rode like that for awhile. I could transfer alot of power through my legs, it felt awesome. Gradually I switched to a more compact form because doing rides over 50 miles in that position was not fun.