Will truing or blueprinting an action increase accuracy that much?

NO, not even with reloads and I don't care what you read on the internet. Spend your money on reloading for it.
I completely agree with you. The problem though with telling the OP to reload for it is that he may know absolutely zero about reloading. Also, there are many that reload who don't know what is involved to building quality ammo. Not knocking anyone, I've been there myself. We all are beginners at some point.
 
I reload for rifles that shoot in the .1's and .2's... Trust me, I know what I'm doing. And a 7mmRM can be capable of shooting however good the rifle can, if the shooter is up to the task as well.
 
I have a rem 700 lr in 30-06. I would suggest a few things first - you can bed the barrel yourself - cost me $5.00 of JB weld and a can of Pam spray on the barrel, took about 30 minutes total. watch videos from gunwerks at youtube. 2. get a good in-lb. torque wrench set from Wheeler in a scope mount kit for about $100.00. 3. I bought a Timney Calvin Elite 2 stage trigger for about $150.00 online - it is worth it's weight in gold! All of these are relatively cheap and easy upgrades. 4. If you want to do more, I bought a Vortex 6-24x FFP scope, just under $1,000.00. Many people say it is as good as a Nightforce for half the price. 5. I found federal TC1 180 gr factory ammo shoots great - the plastic ballistic tip bullets are awesome - try a few different brands.. 6. my gun shoots better dirty - I don't always clean it - (use a fouling shot first). Honestly, the rifle is probably better than me! oh, and practice, practice, practice... using real world condition - shooting sticks, not bench rest!
You bed the action, not the barrel. I would not use JB Weld, instead Devcon or Marine Tex. A proper bedding job cannot be done in a half hour. I admire your willingness to tackle the job, but you tube has led you astray.
 
I saw a rifle bedded with JB Weld once... The moron didn't use a release agent. RUINED the stock and finish on that action. They had to cut the stock up to remove it, and then had to take flap discs and cup brushes to the action to get all the JB Weld off of and out of it, to start the build over.
 
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