It would be easy to say that the player should take more chances with the raises under this rule. I leave the specifics up to the reader.
If the player is to just "wing it" then I'd say raise 4x with any King, 4x with a Queen except not if with 2-4 unsuited [in other words same as normal rule with a K], 4x with 8-Jack suited. Or better of course.
2x raise changes I'd have to think about a little more.
1x raising - if contemplating the kicker situation, go with any Jack immediately, quick with 10 or 9 if possibly in play.
"We thank with brief thanksgiving
Whatever gods may be
That no man lives forever,
That dead men rise up never"
Nor any gambler the long run see ever
........apologies to Swinburne for that last line