The sound of a 5e3 is the sum of its parts. The dirt comes from all three stages including the phase inverter and the power tubes. It is really not the kind of circuit that lends itself to effects loops if your goal is getting a crunchy sound that does not compress the reverb. As a long time user of the 5e3 (and many other vintage fender circuits) I have learned to work with both its strengths and its shortcomings. Try running both channels jumpered and having a reverb pedal into the cooler channel, or experiment with a slapback delay in front of the pre for a kind of "retro rockabilly" fake reverb.
A big part of the reward of the 5e3 is learning to make the best of its strengths and embrace the character that it can give your tone. I believe that the touch sensitivity, the rich chocolatey tone and old fashioned funkyness of its sound can give you so much more than what can be accessed by a more modern, more modular kind of amp.
If the jumpering channels is no good for you, nor the slapback option then perhaps start looking for a more modern (something with more headroom in the later stages of the circuit) style amp.
What you are looking for is something many people want but due to the nature of the beast, have not been able to manage.
Unless you are in the studio....then you can add the reverb in the mixing stage, or if you want to go digital and use a 5e3 impulse etc, or even check out the bad cat unleash.
Having said all that, after playing what would be at least a hundred gigs with a 5e3, once the band is playing, you really don't miss the reverb. Just enjoy the fun you get from the great tone they pump out.