LTVP / PR through marriage & working independently

To work in Singapore (any paid work, incl. self-employed or for remote clients), you need a visa that allows it. LTVP in itself does NOT allow work.
That said, it is possible (but not assured!) to get an LoC (Letter of Consent) from MoM to do employed work while holding an LTVP. As far as I know, there is no such option for self-employment (but you can ask MoM and ICA about this).
The proper, but very difficult, way for that is either an investor visa (which requires millions) or an EntrePass, which you should read up on!
Possibly, your wife could also register a business and hire you on EP - but MoM might reject this if it obviously circumvenes the EntrePass rules.
Once you become PR, you can freely register and work in your own business. But that is only possible a few years after moving to Singapore.

Thanks for this.  Yep, I have studied the EntrePass;  but my circumstances fall in no-mans land.  EntrePass is for business people / innovators who want to come to SG with no existing ties and start a new biz there. The value of the business they bring determines if they can bring a spouse and family with them. 
In my case I should qualify for LTVP on account of my SG cit wife moving back to SG and having employment.  So I don't need to "buy my way in", as I'll be there already. But I do want to keep paying myself from my existing Australian business.  I can do that two ways: 1) keep operating the biz in Australia and transfer the personal payments to me in SG, or 2) set up the same biz in SG and close it in OZ.
I guess in these circumstances I should have a chat with MoM and see what they advise.

Better talk to ACRA, which is the government office in charge of private enterprises. MoM only deals with employees and employers.
If you find a solution, especially if different from what I wrote above, please come back and post it here for the benefit of future readers.