Redesign circuit to use LM317 instead of MFC 6030
Most likely yes, your going from 20V-rms down to 13.8V so a 2A voltage regulator should be able to do that, but there is a caveat.

The voltage drop, which is 6.2V at full load with 2A that will be 12W (which may be a little lower if the 20VDC is really 20-18V or something like that). So if you do get a regulator, its going to have to need a package to handle the heat. 

A simple (inefficient) AC to DC power supply circuit looks like this:


Source: https://www.elprocus.com/steps-to-convert-the-230v-ac-to-5v-dc/

Which you already have the transformer and rectifier. The stage you will need to replace is the regulation stage, which in your case is done by Q1 and IC-1

There are probably better ways to handle this circuit, just ditch the whole thing and get a 13.8V wall wart that can source 2A, I'm willing to bet this circuit is not built up on a PCB to UL standards today. If you buy a wall wart this will be tested and will be less likely to kill you or burn your house down. 

The last thing is they do have DC to DC regulators that are drop in replacements for voltage regulators, then you wouldn't have to deal with the heat.