What I suggest is you may want to split your signal into two, apply the effect to one of the splitted signal and keeping the other clean, and combining them again before going to your amp/DI. This way you get to keep the integrity of the original signal/tone and still apply effects to the overall sound.
To do this, the only simple, readily available way I can think of is using a Boss LS-2 Line Selector, which you can use as an effects send/return and patch the other side into itself... A bit complicated to explain here but it'll work. The other way is if you're good at electronics, get a metal casing and parts from Sim Lim Tower, and make a box (with input, output and effects loop)... with a blend knob on it even better, so you can control the ratio of clean/effected signal mix, and that'll be your solution.