Overdrives belong on amp in due to their design and intended use.
The amp loop is for time and modulation. Not knowing what sort of stuf you record or the style. Since you are a studio guy I would suggest the Lexicon M200 which is only like $200 but has the best reverb, nice delays and some modulation presets. The Lexicon reverbs for my tastes are the best for all sorts of uses and this unit can be used in many different ways.
Problem is I believe the unit is designed for balanced TRS and your loop is no doubt unbalanced. Now I believe the unit will accept unbalanced as I remember the manual. The reason I suggest this is because Jeff Beck used a Lexicon for his reverbs on the Live At Ronnie Scott's effort and his tone is glorious.
The M400 can cover a lot of bases, rackmount but it is Lexicon.
A really nice pedal is of course a good delay which is made for the loop.
I use the tc electronic X4 delay/llooper which has so many modes and features as to be perhaps the most optioned delay around. tc just released the beta of their public toneprint editor which allows you to create your own personally designed toneprints, the unit holds 4 of them. The available internal params inside the unit are beyond anything you would imagine in a pedal. Complete control over delay up to 7sec in all modes. Modes are of course just taking the delay line and artfully using its filters and dampening along with various modulations to sound like tape units or pristine 2290
delays. Another choice of Mr. Jeff for delays is an older 2290
There is a vast array of modulations you can apply to delays, or turn off the delay time line and turn the pedal into a total chorus, flange or vibrato. There are 3 chorus types including a 6 param Tri-chorus, 3 Flangers (I think) and a vibrato.
One can also map the knobs on the unit for any of the params controlling their response curve and limit or range their adjustment effect. Possible to increase feedback w increase delay times or anything you could imagine. Increased and decrease something at the same time on one knob or any of them.
Personally I am fond of the BBE units and have used them for many years now. There are unbalanced and balanced models depending on application. One guy was running unbalanced into the higher end TRS/XLR unit and complained he did not like the sound. Usually when I read someone disliekd the unit it is because of it not being used right or placed in the right spot. It is not an effect so do not turn the processor up much passed 12:00. Makes anything clean or dirt have more punch an tightness in the low end and clarity in the high. Many mistake these as some equalizer thing and that is just not the deal. Helps to read sometimes.