trumpets are loud, but very directional. When you say 'de-bleed' do you mean you're just EQing, or some other process. Vocals, piano, flute and trumpet is everyday stuff and I have never had to do what you are doing? If we assume the vocalist has the mic on the lips, that just means the flute will be the source that gets compromised by the trumpet. The mute is a tonal change device, not really something you pop in to reduce volume, though of course it does. If the trumpet is in the vox, then the singer's mic needs orienting so the trumpet is in it's deader spots and the trumpet playet needs more separation, or maybe one of the small circular perspex screens - although you say he's not too loud?
As the loudest source, there should be no issue adding reverb - the fact the bleed into the vox mic is reverb less should not matter. If you want, you could let us have a listen? that might let us assess the tracks and what is preventing a normal mix. I'd normally have no problems with such a small number of mics, so something odd is happening?
Do you mean the piano pedal thumps loudly when pressed/released? It's normally a very quiet sound - rarely an issue when playing in an ensemble - and is usually right down the bottom, so a gentle roll off easily fixes it?
So, in a room the size we are in, the trumpet is actually omnipresent, and not very directional with respect to the mics.
When you ask about de-bleeding, no it's not EQ adjustments. I have a number of tools and techniques to de-bleed
1) For the trumpet, I use Melodyne Editor in Polyphonic mode. When I bring up the file, you can actually see all the notes that the trumpet mic picked up. If you are familiar with Melodyne, you will know my lingo here, but the musical notes in the wave file are represented by a blob on a piano scroll. The louder notes are larger, and the quiter note are smaller. It's very easy to tell what notes are the trumpet notes just by looking at it. I simply delete the smaller blobs. End result is just a trumpet sound without anything else. I need to be a little careful with this though because secondary and tertiary harmonics come in and are some of the smaller blobs. I do get some artifacts as well
2) My second method is to use Izotope RX de-bleeder. In the tool, I can run an analysis between a file that has some bleed though against the source of the bleed. I typically use this on the Vox and flute files for de-bleeding the trumpet. It works pretty well for this as my bleed source file (from step 1) is almost pure trumpet. No matter what, I still get some bleed, but it's alot more manageable. I do get some artifact if I get too aggressive with the settings.
3) My third de-bleeder is Izotope Music Re-balancer, and I use this primarily for the piano when I have to. This is also a very cool tool. I run an analysis on the file, and I have 4 options to re balance. Vox, Drums, Bass, Other. I can literally go into the file and I can readjust the the volume levels of each of the 4 options. If i turn Vox, Bass, and Drums to "off" the only sounds I get is Other, which is the piano. This method works well, but does leave artifacts as well.
Do not assume vocalist has lips on mic. The singer is typically a foot to 18 inches. Gotta remember we are in a church performing a church service, not a recording studio.
The trumpet is playing away from all of the other mic as well. (Edit: trumpet is off axis for all other mics)
I'll have to disagree with you on the reverb comments. In many cases, I like to put a thick reverb on the trumpet to soften it up a bit, and put it a little further back in the mix. If I have trumpet bleed through in other mics, I simply can't control and set the trumpet back as easily.
As far as the pedal noises, yes when the ensemble is playing, it's not an issue, but if the piano is doing a solo intro it's an issue.
Cheers
