>> Is a gauge needed to set/check the relief valve?
Not necessarily. My personal experience has been that I was not actually able to set the pressure so high that it can damage a cylinder. I've blown the bottom off of cylinders, but not with the valve set too tight. That is probably because the spring inside is only going to push back so much against the pressure you matter what.
But, I full well know that there have been many, MANY small differences in the travel valves released over the years, so your experience could vary.
It would seem that if your pump is strong, and it appears so, that your particular spring is just relieving all the time, or, anytime you activate the valve. It could also be that you have internal leakage in the O-rings. The first thing I would do is get under it and make sure you have full travel on the spool each way. Next, with a blade on the front for some loading, I would turn up the relief valve for that spool by one full turn clockwise, then see what happens. If there is no change, I'd go another turn, but if that makes no difference at all, then I would be disassembling the valve (or just replacing it quickly with another as a test).
As far as adjusting without a gauge, I usually have done it by seat of the pants. I want my blade to be able to very easily lift the tractor with down pressure, and you would want it to lift at least 50 additional (or so pounds) without relief. I've had tractors that if the front blade was hooked under something heavy, you could lift the rear of the tractor off the ground without anyone on it or additional weight on the rear. You should be able to hear it relieve,... it should squeal a little, at least all of mine have.
If you get that thing adjusted correctly though, you might just decide to change tractor colors across the board ! Lol !