First off let me say I have loaded a lot of 308. I used to shoot a match tuned 308 M1 for high power and have a Remington LTR. I've sent a bunch of 155 and168 SMK's down range. I sent a few 175 SMK's down range too but mostly the 168's.
I did not find the need to go much past the shell holder touching the die with the 308. (I do go 1/4 turn past touching for 223 though) I use an RCBS press. There could be a slight issue with using the Dillon although I know folks who load their match 308 ammo on Dillon’s.
I have two sets of dies, one a match Hornaday bushing die which allows me to adjust neck tension by changing the bushing. The other die set is the Forester National Match dies. For the bolt gun I use the Hornaday size die.
I am not interested in brass life but rather uniformity. I full length size every time. The LTR is an easy ½ MOA gun without working at it very hard.
I use RCBS case lube 2 on a lube pad. Yeah it’s messy but I have yet to stick a case and it does wipe off with a damp rag.
I check brass I’m going to use in a match and ensure the case chambers without issue before proceeding to powder and bullets. I don’t check every single case but a random sample from the sized brass. If everything goes OK and it always has I continue. After powder and bullet, I don’t crimp a SMK. I use neck tension alone. This includes 223 used in a match AR. After the ammo is loaded again I take a sample of the loaded ammo to make sure it will cycle through the rifle.
Building a dummy round is a very good idea because for me I can set up my non match seating die up quickly. I like and use the Forester Ultra match seating die for match ammo and they work well.
Take it one step at a time and figure out when and why your reloads won’t chamber. I’m sure it’s going to be simple. Recently I had a heck of a time with some stupid 30-30. I wasn’t chamfering trimmed brass enough. Seating the bullet was crushing the shoulder.
I guess my other thought is, is the die in spec? Good luck.
God Bless our Troops especially our Snipers.