For me, this is more of a money question then a performance question. If you can afford a custom action of good reputation, you will get an exceptional product. However, do you need one to fire these cartridges accurately, NO.
I have built two very good shooting LR "custom" rifles using the Enfield P14 action. Yep, an action designed and built almost 100yrs ago. I have one in 300Wby and another in 300RUM (just starting on the final stock). The Wby shoots sub MOA at long range and it looks like the RUM will too. Total investment for both rifles, under $1000 Cdn complete without scopes. With a tuned orig. trigger, they have a 2 to 2 1/2 lb single stage pull. There are some aftermarket accessories if that is needed.
If you have a Rem700 in the long action, you can make a superb rig for any case that has a reg. mag. head (RUM, H&H, Wby, etc). Many BR guns are still based on this action. There is disagrement if the bolt face should be opened up for larger cases.
A savage 110 action is also a very good platform. Doesn't get less expensive for a new action.
For the bigger cases like the Ridgy, you can modify the Enfield P14, or use a Sako, Wby, or CZ action. There is a Savage built for a few of the Lazz. cases so that is also a possibility. Commercial actions are strong enough to handle our biggest cases (no 50BMG's of course).
The real area for getting performance comes from the barrel, and how it is installed. Of course, the stock and how it fits you matters alot too. All the action really does is help us make the case go bang. As long as the lock up is straight and tight, the trigger crisp and light, the rest of the action's functions are pretty academic.
Optics will play a much bigger role on accurate long range fire then the action will. So, figure out if "custom" is what you want and spend accordingly.
I am very happy with my "antiques" and now have lots of money to spend on good bullets, optics, and powder.
Now if I could afford a Ferrari, would I buy one? Without a second thought.