Big Block seems to slow

There are no fundamental design flaws with a 361 BB Mopar that would make it unresponsive to the normal hot rod treatment.
Compared to most other engines of similar displacement it has heads with bigger intake valves and ports, and a bigger bore.

As long at the basic engine is mechanically “good”, (no broken rings, heads aren’t trashed, etc), a well thought out combo should easily be able to equal(or slightly exceeed) the power output of a stock HP 383(335hp).

However, if the basic long block is pretty tired and will need refreshing, at that point it might be worth considering starting with more cubes to begin with(from a hp/$$$ spent standpoint).

A lot would depend on what your capabilities are, and the resources readily available to you........ along with what the actual condition of the engine is.

I can tell you this, in the 80’s I re-ringed several “very well used” BBM’s that ran really well afterward, especially considering what I started with.

I guess in my mind the make or break point for a 361 would be whether it needed pistons or not.
If the pistons and bores were so bad a re-ring wouldn’t be feasible, then I’d start with something else.

Edit- I just did a search and see that a place called Falcon Performance sells coated cast flat tops in a .040 oversize for just over $400.
So apparently there is some demand for them.
Other than that, all I saw were silvolite dished truck pistons which would have rather low compression and take an odd ring pack.
Customs could be made, but for less money........I could likely find a 440 core.