From my perspective, as an Irrigation DIYer, and someone who HAS tunnelled under a driveway in heavy clay mixed with alabaster rock, here's the points I think you need to consider:
1. For the typical home owner, a 1-1/4" Sch40 PVC pipe is only going to lose about 1 psi / 100' of pipe or less. So your pressure loss in a 300' pipe is going to be about 3psi. This assumes your flow rate isn't going to be greater than 14gpm. But even at 20gpm, the pressure loss only doubles to 6psi.
2. Paying someone to tunnel under your driveway is going to cost $$$. Depending upon the size of your drive and the room you've got to work with, my best educated guess is that the price would be in the gross neiborhood of $300-$500.
3. You can do the job yourself. I did so going under an 11' wide driveway with only 5' of room to work. But I would say that it took me 40 to 80 man-hours to get the job done. You can read about my saga
HERE, and I can provide you with some suggestions based on my experience if you want to go this route.
So given that an extra 300' of mainline isn't a show-stopper with a 1-1/4" mainline, I would say it comes down to where you want to spend your time and money:
Little Time + Lots of Money = Pay Someone to do it.
Some Time + Some Money = dig a 300' trench.
Lots of Time + Little Money = tunnel under the driveway yourself.