The input resistors at U2 are way to low, this is the reason for the large capacitance needed. Depending on the model for U2, it may work with with more realistic values to.
Anyway the LM317 is not really a good choice for a lab supply. Already using the extra transistors to get more current is something that might work, but is not really recommended - especially with changing load impedance. So if you need external transistors the LM723 is the better choice than the LM317, and it already has provisions for current limiting.
The simple standard lab supply circuit also only needs two OPs, a reference and the power transistors. So the circuit above does not even same much by using the LM317.
For simulation I would do the main simulation or the regulator starting from a DC source, so doing the rectifier simulation in a separate step. This allows to use AC simulation (e.g. for output impedance) and thus better check for instabilities.