The loose screw that you mentioned was the cause. It allowed the trigger assembly to move under pressure from the bolt, and when you lowered the bolt it pushed the sear out of engagement allowing the striker to fall. Tightening it cured the problem as you noted. Even the factory tech's are human and probably missed tightening the screw when they had your rifle broken down for repairs...
I have a Savage M110 in .300RUM. It was the first Savage I'd ever had and I worked with the trigger until it would do the same thing that yours did. I then increased the sear engagement until it held a 3.5lb NRA trigger weight, which is just right for such a gun/cartridge.
I don't shoot or hunt with mine much, but when I do, I really enjoy it. I've taken deer out to over 400yds on an airport I have permisison to hunt on and you never know where the deer will cross. The .300RUM is tailor made for this mission. I sight mine in w/180gr bullet at ~3,300fps 3" high at 100yds for approximately zero at 300yds. I hold on top of the back and have made DRT kills at 1/4mile.....or slightly more. Mine kicks a lot less since I fitted a "Kickeze" recoil pad to it. That, and filled the hollow butt stock with urethane foam sealant.... helped with the hollow stock sound...
You can reload for it very economically. Get some of the mil-surp. powders available from either
www.gi-brass.com or Widners shooters supply from pulled down .50BMG.
I bought 16lbs of WC-860 powder back in 2005 for $50 plus the then $12 hazmat fee. They now have some WC872 which is similar but price is higher. I still have over 12lbs of powder, and I've also been feeding it to a .257wby.
I've found that for general purposes the 180gr Remington Corlokts are about as good as anything and when I bought my bulk purchase were the cheapest bullets available. Not anymore..... you can occasionally get Hornady "blems" from either MidwayUSA or MidsouthShootersSupply.com. Either way, I'm shooting the .300RUM for less than I can shoot the .30/30 unless shooting my cast bullets.....
You can also easily load the .300RUM down to either .300winmag level or even down to .30/06 level. It's impossible to make either of those a .300RUM however....!
Try the 180gr Hornady SST over either 87.0gr of IMR7828 or 92.5gr of RL25, or 100.0gr of Retumbo. You'll likely see 3,350fps or more from that 26"bbl on your Savage .300RUM. I do......!
Be sure to use Federal #215 magnum primers..... and Remington brass. The Federal cases hold almost 5% less powder than do the Remingtons..... And a Remington M700 doesn't have the "free-bored" chamber of the Savage so it gets about 100fps less than do the Savages......
200fps if the Remington has a 24"bbl as some do.... Not bashing the Remington's; got quite a few of them.... just fact.....look at the difference in the Speer #8 data vs. Hodgdon's data..... a real eye opener. With a Remington M700 and 24" bbl, the .300RUM is slower than the .300wby w/26"bbl. However, the Savage with a "Weatherby" free-bored throat (0.375" freebore as the Savage has) and a 26"bbl, the .300RUM matches or exceeds the .30/378wbymag.... FYI.