We have 4N as a fake keycard. I think that we can all see that this can't actually help our decision making, since no likely response will tell us anything useful.
We have 4N as a general slam try, but the fact that only one poster suggested it, and another one proposed 4N as keycard, reveals the dangers of using adjective bridge. Partner often has a different understanding. I will say that I think that 4N as a general slam try makes sense, in that we are relatively more likely to want to use it this way than as keycard. However, I doubt that many partnerships have discussed this and this is definitely not an interpretation one would expect even a good partner to assume absent such discussion.
We have 4♠, but the flaw there is obvious. Partner is odds-on to pass, since this is NATURAL call. It is exactly how one bids with 4=6 in spades and diamonds and a willingness to save/bid game to make in diamonds, while checking back for the 4-4 spade fit. This is a no-brainer and those who chose 4♠ have allowed their desire that it be a cuebid to completely override common sense.
We have 5♣. While that should, I think, be forcing, I would be worried that partner may disagree. And even if he didn't pass, I fail to see how our 'cuebid', if he sees it that way, would help him make a good decision.
I think it therefore gets back to making the decision now, without help.
We have posters thinking that slam is odds on, so they bid it. We have posters thinking slam is against the odds, so bidding 5.
I still cleave to the view that partner's 3♥ call suggests a hand that makes slam a relatively poor choice. I'd guess, and it is a guess, that slam will be cold about 25% of the time and would be making on the lead about another 10-20% of the time and would be down a little more than half the time. So I stick with my 5♦ without a lot of conviction.
I would change to Phil's 4N in a heartbeat if I were allowed to announce: 4N, general slam try

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