Boring a 352 to 390 is safely and easily done. When a 390 crank and pistons are installed, you have a 390. If you have access to 410/428 crank (1 UA or 1 UB) with appropriate rods and pistons, it will usually support at least a 410. Since the pistons will not be off the shelf (most people don't know about or shelf stock 410 pistons, especially in a forged) expect to have to wait and possibly pay more than you would for stock or std overbore 428 pistons...that where the temptaion really starts to settle in for most guys.
The problem comes in when or if you attempt to bore the cylinders to make a home-brew 428...don't try it! Some blocks will take the bore, but the walls will more often than not be too thin for reliable performance use. It may not hit water on the boring machine, but a few months down the line, you may have an overnight visit from the Water sprite...The extra few inches is just not worth it.
If you are smart, either get the factory (or aftermarket equivalent) 3.98 crank which will give you a 410 or, if you just can't live without the extra inches...Get one of the long stroke (cast steel) cranks from Scat at 4.125, you will be slightly smaller than 428 and the added stroke should do great things for torque. It'll cost ya, but if you want a big bore FE using the stock block you have to think stroke not bore...after 40 some years of use, the stock block should be expected to have some issues if the walls are thin.
Just one opinion. As they say, "Your money,...your choice".
4.05/3.98 = 410
4.05/4.125 = 421
4.05/4.25 = 438
Note: ain't bench racing fun
? All those toys, it's just like Christmas. All you need is money, effort and skill.