Even if you have 32-bit factors the number may not be the product of two 32-bit numbers. For example 2^62*3 cannot be split as either (2^32, 2^30*3) or (2^31, 2^31*3). In both cases one factor does not fit in 32 bits.
Working on coding it up... it converges to 17±0.5%for N=64 bits in a javascript implementation relatively quickly, but for N=96, it really slows down as Pollard's Rho starts with large factors. This means my fast-and-loose assumption that "a constant number of iterations of Pollard Rho would work" isn't actually true!
Basically, replace the Pollard Rho partial factorization with a method of Kalai [1] for generating random numbers _together with their prime factors_.
I'm able to run this at about 30 samples per second at 160bits, giving an estimate of ~14.1% of 160-bit numbers factoring into two 80-bit numbers.
[1]: https://link.springer.com/article/10.1007/s00145-003-0051-5