Conventional method for mounting the CRT in a cab will work fine. I've done it with 27" Sony PVMs which must weigh at least as much as your 32" (because of all the extra electronics and shielding) and yes, the Trinitron tubes weigh more than normal tubes because they use an aperture grill instead of the (lighter) shadow mask.
To mount the CRT "conventionally", all you need are four pieces of decent offcuts from a strong wood like 3/4" plywood, which incidentally is what I prefer to make cabs out of, so there is always plenty lying around. The four wood offcuts only need to be maybe up to 3-4 inches wide and a bit longer than the side of your monitor
The first two wood pieces are just for blocking. They just need one straight edge and are screwed into the side of the monitor bay at the angle you want the screen to be.
The other two wood pieces will bracket the CRT, and the weight will rest on top of the blocking pieces. To let the brackets snuggle up to the CRT corner pegs, cut part of the wood straight at roughly 45 degrees (like shown below). This will give you some wiggle-room, as the angle will always come to the corner pegs optimally. You can then just slide the two pieces to the tube so that they always fit perfectly.
This design has another advantage - if you cut the 45 degree angle part long enough, say up to two inches, it is easy to swap out the tube for another one of similar size. You just slide the wood brackets up and down to find the right spots for the CRT pegs and drill a new hole

The CRT in pics above is resting very happily there, even though it is not bolted down!
Use T-nuts like these to secure the tube:
I have posted those same pics elsewhere, sorry to people that have seen it before :notworthy You'll all be glad to know that I am finally progressing that cab further.
You can use this same mounting method with commercial metal arcade monitor frames because they will have mounting flanges on the outer edge. I like that you did your own steel frame, you must have some welding skills

However I'm not sure you can use the frame to mount your TV in the way shown above, without some modification.
EDIT: Is that TV *really* 170 pounds? I would have guessed it to be no more than about 120.
EDIT2: I just looked up the user manual and OMG you are right, thus massive beast is listed as weighing 79kg or 175lbs!! That really is a monster.