I've not done any Performance engineering work on the B737, thus my reply carries this caveat, but I can see no problem in operating as you suggest, i.e. using the QRH V speeds (with the required adjustments that you allude to), and an assumed temperature of 50°.
The QRH, Airport Analysis, and FMC speeds are all approved speeds. Using a thrust setting higher than required is a little akin to using the (assumed temp) thrust required for the Airport Analysis RTOW limit at, say, 10 knots headwind, but actually operating with a 20 knot headwind.
The reason that the airport analysis 'stops' at 50° is PROBABLY because that is the Environmental limit for the engine/s, i.e. ISA+35° at Sea Level. In some aircraft (e.g. B777), to address the case where actual weight is less than that available at the Environmental limit, the Airport Analysis continues beyond that limit (e.g. 60°), and data typically has an "A" suffix, where A = Above Environmental Limit. This does not give approval to operate in actual temperatures above the environmental limit, but to further reduce the thrust as though the actual temperature was above the limit. In this case the FMC speeds become invalid, and the Airport Analysis speeds must be used (FMC and QRH usually stop at the environmental limit).
Then again, the Airport Analysis may stop at 50° is simply because the RTOW provider has used a 'practical' range of Temperatures and Wind Components, to avoid using foolscap sized pages for the A/A book. The A/A RTOWs that I produce range from +10° to ISA+35°, to contain the data within practical limits. (If the actual temperature is <+10°, simply use the data for +10°. If it's above ISA+35°, don't fly).
That explanation may make sense, and then again it may not, I am not B737 qualified. To answer a question with a question, what is the Environmental Limit Temperature for your aircraft?
Regards,
Old Smokey