What to do about a no win situation of performance punishment?

You have already asked for more compensation, and been told some rubbish or other. Personally I would take this as an offense as I expect work to take care of any needs I tell them about without fluffing about. Your mileage may differ. If remuneration is a stopping point for you, you should start job searching as this will give you three things.

One, you will find your actual market value, in comparison to what you think you're worth.

Two, you may find a job that you think is a better fit for you.

Three, a job offer in hand gives you enormous leverage in a negotiation if you are as indispensable as you think you are.

The downside of this sort of negotiation is it makes them think a lot more seriously about replacing you. A good manager would have sorted it out without it getting to a negotiating stage.

Corporate guidelines are guidelines. They are not requirements that must be followed or the world turns into some "Mad Max" like post-apocalyptic and dystopian..... (enough histrionics)

The point is that they (HR, Management, etc.) can create a new title. It might not be quick or without going through levels bureaucracy and politics.

What you are describing is being caught between career growth and a lack of a defined path at your current company. Making the point that in a field that is changing as quickly as dev and with someone like you that has domain knowledge, that the current "guidelines" place an artificial ceiling on your growth.

Making the case that going the management path to you will give you recognition of part of your skillset, but also cost the company of the value of the part of your skillset that is most unique.

Consider writing up a job definition that you are suggesting to them. Giving them a job definition and the case why you should be promoted into it (all you wins, etc.) demonstrates that you want to stay with the company. It is much better than walking into your manager's office or HR and saying "I want a raise or I'll leave".

... I'm their only option for many projects

That is your strong point. Explain simply that if you burn out, they will be in some important trouble. You have about 3 ways you can explore:

1. Negotiate for more money. You already did that. If you continue, it will be seen as begging, which definitely works against you.

2. Negotiate for less work. This will have the effect that some customers will be unhappy, but that is an issue to be fixed by higher management - not your problem. They should not have gotten more customers than they could handle, in the first place. They already bit more than they could chew - and now you have to pay the bills.

3. Follow @Kilisi 's answer. With some serious job offers in your hand (not just promises, but written offers), your negotiation power increases a lot. If the company does not give you at least 10% over your best offer, just go - you are already on a dead road anyway.

If you really want to stay (and don't want to simply do less work):

If HR actually wants to help (but can't for corporate guideline reasons), can't they make you manager (on paper) of your own, one-person, "doing the hard stuff"-department?

This of course requires full backing from your boss, probably their boss and of course HR