Ah yes I forgot that you own in SG as well as 'back home'. Out of interest what do you do with your London place when you're out in SG? Vacant, let?
I think your ideas for a progressive move towards retirement are likely wise. As instant full-retirement is often an unexpected shock to the system

I recall looking into getting a Green-Card, but the idea of reporting tax (to 2 or more jurisdictions a year) and tax on global income really put me off. And certainly if the goal is simply to spend a few months there on holiday a year. Does the US have any kind of retirees holiday visa, or could you get tourism visas, within the rules, that would imitate such a thing?
In your shoes I can't imagine buying a place in continental EU from out in SG. Same way I can't imagine buying in a UK regional city from other than when based back in the UK. The other thing that might figure is CGT on the London place [complex!!]. You used to have to return to your former UK home for say 6/+ months, to re-establish it as your Principle Primary Residence, and i.e. then be entitled to CGT relief during your period of time spent abroad. The rules there have been shifting quite a lot in the last year or two, but perhaps something to consider/investigate. [Though if it's not let, and is your de facto sole UK
property it could be you have nothing to concern you there].
For you, moving back to London might not be any kind of 'surrender', or doing so as you have no other plans. I'd consider it more of a short-term stepping stone. Get home, re-group, decide on the next step, etc. maybe you'd not even need to spend a year there [?]. That was my thinking re: London, and the imagined next move afterwards. Such time in London would be something I'd put up with, perhaps no longer wishing to be there, to gain major logistical advantage. Of course now we just popped back there, and I found myself much more comfortable than I expected... finding the next stop thereafter might not be as urgent as I had imagined... ? Quite fortuitous really, as given the cost of moving etc [you've seen the new stamp duty rates!?], moving home and then realising you've made a mistake would be a dreadful financial toll.