Alex, remember, you cannot harm your amplifier if you completely remove the grid-load resistor. With a transformer, runaway from DC instability is impossible. There is always a DC path through the secondary ... as long as the secondary is intact.
If you have an oscillation lurking in there, at some high frequency like 5 to 20 MHz, that's a different story, and unrelated to the value of the grid resistor. 5 to 20 MHz oscillations, even at a very low level, will absolutely make the sound bright and unpleasant. If they are -40 dB down, you will never see them on a scope ... that's no more than a trace width. You need an RF spectrum analyzer to sniff out the little monsters. They look like little spikes rising out of the noise floor (which should be very smooth).
If you suspect this, you need a grid-stopper in series with the grid pin, like 100 to 500 ohms of carbon-comp resistor soldered no further than 1/2" from the grid pin. (NEVER use a wirewound for a grid-stopper.) That will kill self-oscillation.
I would try a grid-stopper first before futzing around any more. The only way you can solidly rule out self-oscillation is use an RF spectrum analyzer that's good to at least 20 MHz, preferably 100 MHz. These things aren't cheap, and only have one use, chasing out RF nasties. Low-level RF oscillations are surprisingly prevalent in high-end audio equipment, with poorly designed regulators as the usual culprit.
Try the grid-stopper first before anything else. After that, play around with various value of grid resistor, including nothing at all. It should not be sounding bright, unless something is wrong.