It's not really as simple as scooping some mids! The 5E3 is very low end heavy, not midrange heavy. And BF amps still have plenty of low end too, just not as much as a 5E3.
There are a few very simple things you can do to the amp before you even get to the pedals. Get the amp sounding right first before trying to apply a bandaid. I have built many 5E3s and my favourites are those that I have built to be properly biased and with some of that huge low end addressed. Nowadays i use a PT with a lower B+ which makes it easier to bias correctly but you can still bias a 5E3 correctly with the stock transformers. Because wall voltages are so much higher now the bias is usually way off and the 250R cathode resistor is no longer the right value.
It is unlikely that you have your amp biased to 100% plate dissipation with the stock 250 or 270R bias resistor. It's probably more like 120-140%. That will help your power tubes to wear out faster and your tone to actually be a bit brighter than it should be. I think Rob Robinette describes how to check the bias - it's not difficult. As the amp is cathode biased it just involves buying a few 5-10W resistors in various values - starting from 270R (250 is difficult to find these days) and going up to maybe 470R. I use ~10W Dale resistors from Mouser. (They look really cool!) I can tell you how to measure everything if you need. Note biasing to 100% plate dissipation is only recommended for cathode biasing. For fixed bias amps I usually prefer around 60%.
Once the amp is biased properly it will sound so much better and break up in a more musical way. I see you are using JJs - good choice. Just remember that JJs are rated at 14W rather than the 12W most 6V6s are. This is important when biasing.
Next I like to reduce the value of the coupling caps. I think in my last 5E3 in ended up with the first three caps at .022µF and used .033µF for the PI caps. It sounds drastic but you still have plenty of low end but a vastly more balanced sound which again, breaks up better because it's not loaded down with tons of bassiness. You could just replace the first gain stage cathode bypass cap with a 1µf cap for starters if you prefer. Caps are cheap and an easy way to tweak your amp. I like these:
https://www.tubesandmore.com/products/capacitor-vishay-roederstein-630v-mkt1813-axial-lead
It will still sound like a 5E3 but a really good one! Then you can just use all the normal OD pedals you like.
The other thing to look at is obviously the speaker. The speaker has a huge impact on the sound and can dramatically affect how the amps sounds and responds. I like the Celestion G12H Creamback, but there are a gazillion options there, and mostly no more expensive than a cheap pedal.
You can obviously build an excellent amp - the pics show that! Don't be afraid to swap out some caps to get the amp sounding better. If you don't like it it takes minutes to change it back. Everyone who plays one of my tweaked 5E3s seems to prefer it to the stock versions. And FWIW the clean sounds are every bit as good as BF Fender if not better. A well sorted 5E3 is a wonderful pedal platform.
Excellent post, lets talk 5e3 biasing and coupling caps as I think its important info.
First of all, the amp sounds great as is, I'm just trying to see if I can get other Fender-family tones out of it via a pedal rather than bypass or coupling cap mods.
I agree that 100% dissipation is ideal, so to get there with the 14w JJ 6v6s tubes I used a 270ohm cathode resistor on the power tubes, and Hammond transformers as they deliver the correct volts. After the circuit had had an hour powered up to settle down I measured the following readings:
AC Volts at receptacle: 122.1V
B1 379V, B2 331V, B3 243V - which are are close to historical norms
6v6 Cathode voltage = 21.5V
V3 Plate = 369V
V4 Plate = 366V
OT impedance from V3 plate to center tap = 179ohm, with 6.78V across it = 37.8mA
OT impedance from V4 plate to center tap = 243ohm, with 9.69V across it = 39.8mA
Power dissipation V3 = (369-21.5)*37.8E-3 = 13.1W
Power dissipation V4 = (366-21.5)*39.8E-3 = 13.7W
...I decided those were close enough.
I've read a lot on possible coupling cap and bias cap changes, and as I understand it, yours are as follows:
Both V1 -> V2a coupling caps replace 0.1uF with 0.022uF
V2a -> V2b coupling cap leave stock (0.022uF)
Both V2b -> V3/V4 coupling caps replace 0.1uF with 0.033uF
So yes, that will filter out a lot of bass. If you also change the 25uF bypass cap on V1 to 1uF that will do same.
I guess what I'm trying to do is pre-filter the guitar signal so that it has similar effect to all those cap changes.
Finally, I agree on the importance of the speaker, but I went for the '5E3 Speed Shop' A12Q which - according to the forums - is an even better replica of the old Jensen P12R than the ubiquitous Weber 12A125. It certainly delivers! I haven't heard a 5e3 with a Creamback - wouldn't that preserve more middle and bass than a Jensen - clone? I think one of the reasons that a Jensen is traditionally used in the circuit is that it offsets the bass. I can see why you made cap changes if you weren't using a Jensen-like speaker. Have you tried yours with a Jensen or similar?