You are wise to ask questions like this and be cautious. Fortunately you really have to be off to have any major problems with ammunition you load.
****my biggest concern is you are using the Lee book to load the Hornady GMX bullet***
****A monolithic bullet like the GMX bullet is longer and will likely result in higher pressures than a lead core bullet they were using to test the load data for the lee manual.****
I'm guessing that 47 grains is over max. Monolithic bullets almost always have lower recommended max loads. I have the most recent Horandy book and could look up the recommend max load for the 165gr GMX with BLC2 powder if you don't have access to it.
I've pulled hundreds of bullets with a kinetic puller. They work and are safe as long as you aren't hitting the primer against something. If I'm just pulling one or two bullets then I find the kinetic puller is faster. You could pull 50 bullets with a kinetic puller but you would probably save an hour or possibly two hours of work if you use a collet puller.
I've loaded ammunition for over 20 rifles and have been doing it over 20 years and have never seen any serious overpressure signs at max load. This doesn't mean you won't have pressure issues at max recommend book pressures but it is very very unlikely. There are multiple minor changes in a cartridge that you load that can cause unsafe pressure. Different brass can have different case capacities. A heavier piece of brass likely has less case capacity than a thinner walled piece of brass and that heavier piece of brass with a thicker wall can actually be less safe around max loads. Shooting monolithic bullets like GMX or seating bullets "deeper" will result in less case capacity and higher pressures. Different lots of powder or primers can also result in different pressures.
Even though I doubt you will have any issues with the bullets you loaded, I would caution you against shooting them.
***Just because you don't have any issues with max Lee book loads with BLC2, doesn't mean you won't have issues with Lee book max loads for H4350 or Varget.***