Back from Pune! As advised to @Vaseem, I stuck to the regular NH65 route. However, while coming back it was not as smooth as the onward journey due to a lot of truck traffic. Took the same about 12 hours again though. So I would agree with ranger now - it's mostly a mixed opinion on which road to take. If you are not worried a lot about time taken, maybe the Gulbarga route is a safer bet!
Not fully sure, but maybe less than 50% is fully completed. But I found most of the diversion roads in good condition, as those are actually the completed sides of the 4-lane work.
One more aspect regarding pit-stops on the way. If you go via NH65, you'll find a decent bunch of eateries only till Humnabad - Noor Dhaba being the last one (we had breakfast there during our onward journey and a tea break during return), with decent pay-n-use washrooms. However, keep in mind there is almost nothing of that kind between Humnabad & Solapur (on NH65) - so do plan your stops accordingly.
Solapur town has a lot of very good restaurants, both veg and non-veg. Kamat is a good option for vegetarians, and Kareem's resto an excellent choice for non-vegetarians. I would recommend Kareem's for another factor - they have a western style restroom, which I found missing in most other restaurants, including Kamat. With senior citizen parents travelling with me, a western style restroom was mandatory - so we took a lunch break at Kareem's during both onward and return journeys.
Again between Solapur - Pune, there are several other joints which looked good for a pit stop, so no dearth of choices there. About an hour before entering Pune, we stopped at a nice place for tea and snacks - it was a food court type - containing a Sugar n Spice outlet, some branded Vada Pav/Chai corner & a kabab station. And excellent washrooms again :-)
One last advice, keep all your original and up-to-date documents with you (license, RC, pollution, insurance). Both during the onward and return journeys, we were stopped thrice (each way) by the police for a document check. And they did check each document thoroughly.