SEAI Better Energy Grant & HRI/VAT Refund: how much of a saving?

I'll be spending at least 60k renovating my house. I'm trying to see the maximum amount of money I can get back via the Better Energy Grant and HRI/VAT Refund.

Could somebody clarify the following please:

Home Renovation Incentive (VAT refund):

If I'm reading this correctly, the maximum expense on any one property is 30k *before VAT*. The highest tax credit we can get is therefore based on 30k before VAT expenditure meaning we'll get 4,050 back as a tax credit. First, is this correct? Second, do my wife and I now need to register with Revenue to be assessed jointly for income tax purposes?

This refund only applies to renovation etc that is charged at 13.5% VAT (i.e. it doesn't apply to services charged at 23% VAT). Importantly, too, if we spend say 10k on external insulation we will get 2700k from the Better Energy Home Scheme Grant but only 226 VAT back on top of that:

For example -

8,810 plus VAT (at 13.5%) of 1,190 = 10,000 was paid for external wall insulation

2,700 was received under a Better Energy Home Scheme grant External link

The 10,000 will be reduced by 8,100 (2,700 x 3)

Leaving 1,900 (10,000 less 8,100) qualifying expenditure

This 1,900 includes VAT of 226

The tax credit can be claimed on the 1,900 less 226 = 1,674 (before VAT).

The tax credit is 1,674 x 13.5% = 225.99.

So, my third question is based on the above example, and the 30k (before VAT) limit for VAT claims: would it be more financially beneficial to us to not claim the VAT back on the component of our expenditure that is eligible for the SEAI Better Energy Grant wise, and to claim the VAT back on 30k of other expenditure?

Fourth, if I make the claims as above, would I get rougly 30% of the cost of the Energy saving work back from the Better Energy Grant, and 4,050 of the 30k that I will claim in a VAT refund?

Fifth, are there any more grants we could be eligible for? Thanks.