I have also come to the recent realisation this problem is not as bad as it initially appears. So long as we are abolishing other taxes e.g. Stamp Duty, Income tax etc. the falls in land prices and homeowner equity will be in part offset by the increases in land values abolishing other taxes causes. It is well known cutting stamp duties results in higher property prices by ensuring buyers have a larger capacity to pay. However company tax cuts and presumably even income tax cuts have the same effect to some extent. So while we would see prices fall, they would not be as dramatic under a revenue neutral tax shift.
Company Tax cuts:
In the longer run, Australian listed and foreign companies can be expected to invest more, build up the capital stock, and so drive up wages (and returns to other fixed factors, such as land).
Still, there may be losers. Some domestically-funded firms might lose. And if policymakers were to permit migration to grow strongly in response to a stronger demand for labour, wages would not rise much, and stronger population growth would push up rents and land values.
If we were to abolish no taxes and just increase LVT, I think the most amount of revenue you could get would be a bit over $150bn (between 80-90% of current private annual land rent). However as you cut other taxes the amount of revenue raised would increase as land rents and values rise.
On this basis, we could hypothetically immediately raise $150bn in LVT revenue - 25-50% of which would go towards abolishing all state taxes on production (which feeds into reflating land prices), and we could use the remainder to reduce our negative income tax marginal rate in our BI policy, boost Universal Basic Pensions, funding for retirement villages etc.
We could then use a proper Resource Rents Tax regime (e.g. mining tax, petroleum RRT) to offset some company tax cuts - this would help pit the BCA against itself given some of its members would win and some would lose. Then we can wait for the all of the tax cuts to feed back into land rents before raising more LVT revenue to continue other tax reductions.