Force carbonating an almost carbonated beer

Should be fine. You might want to go higher - I'd rather risk a foamy beer over a flat beer. Foam calms down, there is no coming back from flat once it's in your glass.

 

Yes, I was thinking no higher than 30.

 

It needs time, hours not minutes. Keep to your plan to check in a few hours.

 

If it's in a corney keg you could switch the gas to the beer line that way the gas has to travel to the bottom and flow through the beer to the surface. Other wise you'll just carbonate the beer slowly on the surface of the liquid.

 

60 psi in a chilled keg, left alone, usually gets me where I want to be in 24 hours. I realize it's not quite that simple, but I would probably suggest 30 psi for 12 hours. Then vent the excess pressure and see where you are. I suspect it'll be close enough for the intended purpose. As Doug said, it's better to overshoot it a bit than to undershoot it. If it's too foamy, simply reduce the serving pressure to 2 psi. Then vow to keep a closer eye on things next year so you don't find yourself in the same predicament.

 

try shaking the keg. this increases the surface area exposed to gas and I find it really speeds up the process.
and like everyone has warned, here and in dozens of other posts, this deal is a crapshoot. no guarantees. the more you shake the beer the quicker the gas gets sucked in. i usually charge it to 30 psi or so and turn off the gas. then shake until its all absorbed. turn the gas back on until you don't hear it flowing anymore, repeat. a few times.

but high pressure, 30 psi or so. cold beer, 38F. Shake. Time.
Good luck.