I want to pay off my HECS/HELP loan quicker. I know that I can make voluntary repayments but that amount isn't tax deductible. Ideally I want to bump down my pretax income to 37k so I avoid the 32.5% tax rate.
Am I able to ask my employer to allocate a greater sum of my pre-tax income to my HECS debt so that I'll pay it off quicker?
No, you can't use pre tax income to pay any debt (HECS or otherwise)
This is a poor idea. You should never pay off your HECS/HELP debt, it is the cheapest loan you will ever get. You are far better paying off any other debt you have (Credit Cards, Personal Loans, Car Finance, Homeloan) first then saving 3-6 months pay as a rainy day fund before even considering it.
Your income doesn't seem particularly high so even if you have done these things I'd then start saving for a house, it will be a lot harder to pay a larger homeloan with no HECS debt than a smaller homeloan with a larger HECS debt.
Also there's no real harm in hitting the 32.5% bracket, Tax brackets are only on marginal earnings so you only pay 32.5% on the income above $37K, paying the higher rate wont cost you any extra.