Yes sir, however that 44 million only includes a roster of 3 guys (doesn't include the option for Rondo). So even if you took a 12mil FA and a probably very low draft pick, you'd have no bench and you'd have lost two of the best guards in the NBA.
Your second idea is probably a better idea. Extending Ray and Rondo are good ideas, but without a trade of our bench we still won't have decent support because our will cap only allow us to sign a Mid-Level a year, which is a risk at best, and we can't be sure we won't lose more guys to free agency.
Technically, we'd have 8 players on the roster (6 under salary, 1 max player, and the 1st rounder I allocated $1MM for). It would require us to build the rest of the roster with the MLE, LLE, and minimum salaries as well as 2nd round picks.
We'd be over the cap by the MLE, LLE, and minimum salary players AND if Rondo is offered a RFA deal ... that amount over his $3.7MM qualifying offer as well.
I'm simply saying that it isn't impossible to see us going down this route. The flexibility is there. Whether we want to go down that route is another story.