First of all take your time. Beat it from all directions before taking any action that is not reversible. Once you decide, put it in the mental hopper for a month and let it stew and then review the decision. No need for speed.
Personally I would keep it as is. While I understand and have no issues with what has happened in the past with people making them more usable, its time to preserve the good and unusual examples.
Buy a cheap one and convert it if you want .
Sounds like you have a a really great one and keep in mind that stock is probably part of why it shoots well.
No experience with the front tension but it usually was intended to have some pressure on those full stock guns.