Alot of people rate 400TX near the EI 250, and develop it in rodinal. I concur with that, and get good negs with a long tonal scale. I actually prefer more contrast than that combination affords, but it's nothing that can't be sorted out in the darkroom.
I've overexposed 400TX by at least 4 stops on my Holga, and still managed to get wonderful prints from those negs. They needed a lot of burning in, and were as grainy as you could want, but the image still worked. It's hard to overexpose a film like Tri-X. You should be in good shape.
Depending on what metering mode you are using, spot, center weighted, or matrix, you may need to expose at 200 in order to avoid underexposure with Tri-X. You could try taking one roll in and asking for reduced development as you say you are inclined to do, and, depending on how that came out, give the same or different instructions on the remaining rolls. I always shoot Tri-X at 200 in 35mm on center weigted meter mode and develop in XTOL 1:3 @68degrees for 12.5 minutes (this is the time that is often recommended for Tri-X exposed at 400). If I wanted to reduce contrast on Tri-X exposed at 200, I would develop it for 10.5 minutes, or less depending on how much I wanted to control contrast. If the subject or lighting was obviously high contrast, I would at least try one roll at a reduced development time and go from there.
My current formula for Tri-X 35mm is 250, Rodinal 1:100, 20 minutes, 20ºC, 30 sec. initial agitation, 3 gentle inversions every 3 minutes thereafter. Yields long tonal scale and good grain characteristics, but for low contrast scenes you may want to go to 1:50 and adjust the time accordingly.
Honey, I promise no more searching eBay for cameras.
I'm with Mabman on this one. EI 200, 30 seconds initial agitation, 2 gentle inversions each 30 seconds thereafter for 5 minutes total at 68 degrees f/20 degrees C. This was my standard for Tri-X for years.