I have the strong mount. I guess I need to move my press.
There are a lot of ways to achieve stability, and to get there sometimes you need to think "out of the box".
Primary consideration: Due to the way the press operates, you need stiffness (or resistance to movement) up-down, left-right, and front-back. IOW, 6 axes of support in order to achieve a
rock-solid support.
? If you think about it very long it may occur that the only thing on the bench that needs support is
the press. Everything else, the books, calipers, primers, powder, etc. could be supported by the flimsiest of tabletops. So the cheapest thing to do is to build 2 benches side-by-side. One super strong
mini-bench for the press, and then one large
shelf / tabletop to support the reloading supplies, both at the same height for your convenience. This has the advantage of concentrating the cost at the point of need.
? Additionally, while some materials may need to be scrounged up, you should take advantage of existing "stiffness" to reduce your material requirements. If your bench can back up to a concrete block wall or a sheet rock wall with studs, then the existing wall can can be utilized to absorb 4 axes: left-right and front-back. Therefore, the mini-bench only has to be 20" wide to grab 2 existing wall studs. So for the cost of 2 large steel L-brackets to attach to the wall, you've saved a lot of other material costs.
? So then, the only 2 axes remaining to be subdued are up-down. As previously discussed, this is easy to do with a single, heavy bench leg directly under the press. The single leg could be a tree trunk, large treated timber, scrap wood from a shipping pallet, or several 2x4's glued together. This type material is in every construction dumpster; there's no need to buy anything.
? Lastly the new benchtop needs to resist bending. The easiest way to do this is layer 3+ thicknesses of 3/4 plywood. The one on the top (showing) can be nicely finished, but the interior layers needn't be anything more than rough particle board. The secret is to glue (Liquid Nails) all the pieces together and then screw them together from the underside. You can finish it off by adding some nice trim to the edges to help conceal the layers.
? So the sturdiest, cheapest way to go is going to end up looking like this...