I’m wondering how straightforward it’d be to replace the connectors on the cables connecting my pedals with low profile connectors (below).
Then… what do you do about those MIDI connectors? 
GLS Audio 1/4" Right Angle Plugs TS Mono Flat Low Profile Pancake Style for Speaker Cables, Patch Cables, Snakes - Male 1/4 Inch Phono 6.3mm Phone Plug Bulk - 20 PACK https://www.amazon.com/dp/B003UIC78W/ref=cm_sw_r_cp_api_i_9SXeCb8J1WN89
Provided you’re slightly handy and have a decent soldering iron, it’s trivial. Literally two solder joints each. Desolder the existing connectors, solder the wire to the pancakes.
Switchcraft makes right angle MIDI connectors that can save some space, but they’re irritatingly expensive. Most MIDI connections are on the back of things, and there’s generally room behind gear to accommodate, so I don’t think it’s been a problem people see as needing solved for the most part.
I know. It’s just not common enough an issue that companies haven’t dedicated resources to designing and selling a ‘flat’ MIDI plug, and they upcharge the hell out of the right angle ones for the same reason. It’s a bummer, but I don’t know of any real solution to your issue except maybe those right angle ones.
I was able to find these:
Rockgear Midi Cable, 60cm / 23.62" Black https://www.amazon.com/dp/B0781N848Q/ref=cm_sw_r_cp_api_i_0P3eCb4X4NYZ8
For the amount of money you’ve spent on your gear, they look a bit cheap and nasty. could you not go for standard right angle connectors like these?
Pancake connectors are standard for pedalboard connections - robust, low profile, and damn near indestructible. They are in no way “cheap or nasty”.
I was talking about the one’s he had linked to. Maybe it’s shit photo’s, but the look bad to me compared to the Kirlins I use for my pedals or to piggy back the VF-1 and SE 70.
