You kind of sort of already have that. There's an in-game option to "turn off XP" that will automatically convert that XP into influence instead.
Really? Where is that located?
From ParagonWiki, Menu -> Options -> General -> "Disable Earning XP"
As someone else pointed out the 2X Inf is only when Exemplared. (see text below from wiki) So a INF increase would be nice.
Disable Earning XP
Earn XP - Earn experience points as normal
No XP - Disable earning experience points (inf gains are not affected)
XP While Exemplared
Earn XP - Earn experience points even while exemplared
Double Inf*, No XP - Earn no experience points but double inf gains while exemplared