Is this definition of an RSA modulus safe?
Overall I find the proposed definition and methods satisfactory in principle, barring quantum computers usable for factorization; but the 512-bit limit for factor, and to a lesser degree the 2048-bit unfactored limit, are not conservative.



Unfactored limit

As noted in comment, for long term security or/and convincing security authorities, it's probably best to up the 2048-bit size to 3072-bit, or more. France's ANSSI changed mind and went from year 2020 to 2030 for the limit beyond which 2048-bit is no longer enough, but other authorities stick to earlier dates.

Difficulty of factoring $n$ by GNFS grows with $L_n\left[\frac1 3,\sqrt[3]{\frac{64}9}\right]$ in L-notation, and (ignoring the hidden $o(1)$ term) that tells 2048-bit is roughly 40 Binary Orders of Magnitude (BOM) harder than the RSA-768 landmark of 2009. This is comfortable for now, but not huge. 3072-bit gives 62 BOM, that is huge.



Small prime limit

Difficulty of factoring by ECM grows roughly as $L_p\left[\sqrt2,\frac1 2\right]$ where $p$ is the factor pulled. Neglecting the $o(1)$, that tells a 512-bit $p$ is roughly 28 BOM harder to pull by ECM than the 273-bit record of 2013. That does not look like a comfortable margin to me: Ryan Propper's log and account mention relatively modest resources compared to the RSA-768 effort: 


  For this job, I did about 5,000 curves, spanning about 10 days, on the FarmShare compute cluster at Stanford. I guess this was quite the lucky find. :) 


and I do not see that the latest theoretical advances (Edwards curves) have been used. Consider more effort, dedicated ASICs, Moore's law at 1 bit per year, and the 28 BOM is about gone. I would not go below 640-bit (>41 BOM) or 704-bit $p$ (>47 BOM) with 2048-bit $n$. 832-bit $p$ gives 59 BOM, that's large.