the numbers strava seems to think for my power output on recent climbs
Caveat Strava. It's woefully inaccurate. I wouldn't base anything on their figures. I can point at a large number of Strava segments it gets completely wrong for me based on its estimates.
2w/kg
I wasn't far off that when I completed PBP but it took an awful lot of mental strength to keep going.
I'm 96kg at the moment. I can slog my way around a 200 or (probably) a 300 but I really won't enjoy it as I'll be bouncing on the time limits most of the ride.
If I lose 10kg I'll enjoy Audaxing again as I'll suddenly have a whole load more spare time.
If I lose a further 10kg then it's a joy, and I can enter silly rides (stupidly hilly, etc) and/or punish myself by choice of lack of gears/freewheel.
But, be careful what you are comparing. On the flat (i.e. TT-ing) W/kg is a relatively useless measure. TT-ing is all about W/CdA and aerodynamic drag is nigh on impossible to measure yourself. CdA has a strong correlation with weight (since the bigger you are the bigger the surface area you have) but there are some very heavy but fast TT-ers out there as they know how to be aerodynamic.
Grand Tour riders worry about W/kg as most of the time W/CdA does not really matter (TT stages excepted).
Audaxers should generally worry about W/kg but trying to keep aero does help.
TT-ers don't really care about W/kg, it's all about W/CdA.
tl;dr as someone who is 96kg I'd be focusing on losing weight rather than gaining power; the latter will come naturally with the work that is required to sort out the former.
Saying that, I have power meters and the sense of progress/development that comes from slow incremental improvements is a massive motivator for me.