I've done half a dozen wells with the portable drilling rig (Hydra drill? I walk by the rig every day, but haven't used it in over a decade). Gets very difficult to get below 150'. Pumping the fluids down to flush the cuttings becomes very difficult. Going through rock is a bugger, but they do make rock coring bits, and cutting bits. I got in a 'jam' once, and my drill bit broke, going through a 3' section of sandstone. Time was critical (didn't want to have to set casing, and then pull it... otherwise the well would fill in with sediments) so I got some plumbing fittings, welded up a cutting bit, and welded carbide teeth on it. Worked great, saved a bundle in money and time.
But... going thru 300' of rock... it's not going to happen. You'd need a rig as good as the regular drillers, and a high dollar pump, to pump the fluids in and cuttings out.
One of my relatives has a road boring machine, and they can bore through solid rock... but it takes ages to do it (days).
The well I drilled for myself produced good initially, then realized the iron content was too high to use (the water would turn blood red if it set... not what you want to wash clothes with). First year of drought, it went dry. I ended up building an 8 acre lake instead of getting a professionally dug well. Now I have a 6 to 8 year supply of water (if we ever got a drought that'd last that long, sure the world as we know it would be over) and gravity fed water into my house. Gravity flow beats any kind of pumped water.