Took another listen to it with fresh ears. The honk seems to be sitting around 700hz. Kinda sounds like a cocked wah pedal.
The best advice I can give in my very limited experience, so please forgive me if you've already tried it, is try to find an IR or blend of IR's that sounds the closest to what you want from the start. If you think you'll have to notch a bunch of freqs, skip it. I've tried to EQ-shoehorn IRs into what I wanted and it just sounded *****.
And take a lot of breaks to let your ears reset. Some tones I spent quite a while trying to get, thought they sounded great only to come back the next day, again, sounded *****.