Bsek, Welcome to our forum.
You did not tell us the date of birth of your No. 1. The early triggers were fully adjustable and about as good as it gets. Later ones not so much until about 2005 when Ruger made improvements. I bought mine new in 1975, the so called "red pads" with the good trigger. Right out of the box it broke at 3.5 pounds which I consider perfect for a .300 magnum hunting rifle.
The first thing I always do with a new to me firearm is to completely disassemble, inspect and clean every part to within an inch of its life. The thing I noticed was that the beautiful wood was not well sealed on the underneath sides. Multiple coating of diluted sealant with long curing times between coating were applied to better stabilize the wood in varying temperature and humidity hunting conditions.
Next came experiments with loads and bullet seating distance. With no magazine restrictions, it was easy to set it up with the bullet tip just not touching the barrel groves which worked best for my rifle.
As to the forearm, I installed a shim and free floated the barrel.
Now about shooting groups. Realize that were are talking about a single shot rifle, the only important thing is how close the first shot strikes to the scope cross hairs point of aim at a given distance from a cold near clean barrel. 3 shoots are fine with me. Long 10 minute waits between shots are the way to go so you are always shooting with that cold barrel. With the right load and a calm day I always get 3/4" 100 yard three shot groups in the black.
I have never tried firing 5 quick shots groups but suspect they may be several MOA which is meaningless for a single shot rifle unless you are Tom Selleck faced with multiple bad guys.
As to your trigger, I suggest that you leave it alone until you have done the above. If it is really too heavy or creaky, send me a PM.
John
ps, No mule deer has ever escaped my first shot with the Ruger No. 1.