It is unfortunately quite common for meltdowns to result in suicidal thoughts, they're not just quirky tantrums, they're huge neurological bouts of distress and there seems to be a disconnect in understanding and treatment between community care and medical care in regards to how best support young people in this sort of crisis and put preventative measures in place. It's despicable and often ends up with young people either not getting the inpatient treatment at all or not getting therapeutic treatment. It's usually pushed back to community care as it's an acute episode and then pushed back to medical care as it's part of a chronic condition and it's a horrible game of hot potato.
I know it's a drop in the ocean and might seem like a redundant question but have you ever heard of pain stimming toys? It won't solve all of your daughters troubles, but they work by providing the dopamine you're craving when you're in crisis in a way that safely provides pain, so it can be a good step to redirect to before the suicidal ideation creeps in. They are sensory aids, but they're by no means a cure to all of the problems that come from having a catastrophic meltdown. They're best introduced and used regularly when children are regulated and not introduced during the crisis stage.
On the note of the special needs buggy, don't let a lack of funds stop you from seeking an assessment from wheelchair services or occupational therapy, whichever takes the lead for this in your area, usually referred by the GP. What they usually do is say we will offer you this a. Wheelchair or b. Bog standard disability buggy, and you can say yes or no, it needs to have a 5 point harness, able to hold up to 9 stone, recline as it's the only time she is able to seek rest, have a sun shade to prevent sensory dysregulation, and weigh enough that she can't tip it over by kicking back and they will say well it costs ££££ and you will have to fund some if not all of it, and then you take the offer to your local regions pushchair/wheelchair charity services who will do a cost assessment to cover the costs bar any additional add ons like transport hooks etc. I'm simplifying and it's charity dependent, but I'm going through this exact process right now with DS. Newlife and Caudwell are really good charities for this.
It sounds like she might also benefit from a safe bed. I am generally against restraint, but safe beds have their place and this is what they're for. They prevent children from causing mortal harm to themselves, and minimise risk. They're designed to be tear-proof and it means you can safely leave her unattended at least to sleep. There are also charities that will fund partly or fully for these.
On the sleep note, I might have missed it, but how is her sleep? If her sleep is poor, ie. Doesn't sleep while late, wakes too early or frequently wakes at night then a good next step once you've got a management plan for her meltdowns would be to ask for an urgent referral to paediatrics for a sleep assessment where they may be able to prescribe melatonin. Having poor sleep sets you up for a lower tolerance to sensory input, so meltdowns can seemingly come out of nowhere with no apparent trigger, when it's really the accumulation of so much overwheln and a lack of bandwidth to deal with it all. She might not even know herself that the reason she's so distressed is because she's trying to process all of this sensory input all at once all of the time because it's a hard thing to recognise. It is something to bring up to which ever medical professional accepts responsibility for her care if this is an issue you have.
I know social services have said they can only offer for her to go to a relative short term, but have they actually offered you a parent carer needs assessment to see how they can support you to support your daughter, or your daughter a child in need assessment when she is actually showing signs of being in need? I think she would qualify under section 17.
Sorry if I'm repeating what others have said as I've only read your posts.