Should I skip UK altogether and wait 6 months before re-entry?

You completed a YMS tour in the UK and have been in the Republic since then, and you contemplate returning to the UK but have reservations (well founded).

To be honest, a British Immigration Officer is likely to see your premise as a contrivance and that you have a secondary agenda which you are not disclosing. Looking at your premise...

I'd love to go back to the UK for private medical care,

You will be asking them to accept that a mobile and active person is twelve time zones away (repeat, 12 time zones away) from home because adequate medical care is not available in Australia. This does not fit the profile of a genuine visitor of either the leisure or medical kind. They will ask questions like...

• Did you declare this condition previously in your YMS application?
• What treatment did you receive in the UK during your YMS visit?
• Did your UK doctor tell you to come back for more treatment?
• Why did you not seek treatment in Ireland? Weren't you just there recently?
• Do you have correspondence between your Aussie doctor and his/her counterpart in the UK?
• Do you have anything that shows treatment for your condition is not available in Australia?
• If you need medical care, what stopped you from returning home after your YMS was completed?

to obtain business tax lodgement advice and close of my personal HRMC tax too

Many people never lay eyes on their business tax adviser. Mine, for example, is in Birmingham and I've never seen them face-to-face. It's an email thing. IO's know about it...

• Who is your tax adviser?
• Why do you need personal contact with him/her?
• Where are they located? May we see your accommodation arrangements for that place?
• May we call him/her and enquire about the nature of your visit?

And the big one...

• Given that your YMS is completed, why have you not returned home?

And again, you have explained this...

So, I thought, if I travelled to asia for 2 months, perhaps after 5-6 months had passed, I would be permitted re-entry to the UK?

It's not the way genuine visitors approach things. First they define their premise and then that dictates when they need to enter and re-enter. Your approach is the reverse. It's more like "...if I try 'X' will that work?...". There's lots of similar questions like that in the archives here, mostly asking if the length of their proposed visit will work or if they put such-and-such a premise will it work better. Honestly, define a genuine premise and all the other questions become irrelevant. I'm not saying you actually do have a secondary agenda, but for sure it's what the IO will be thinking and your rationales look very weak.

Your other question...

Or is that 7 days counted as a new time-start, cancelling the 3 months I've been out of the UK?

The UK is not like Schengen where each person has a clock measuring when they were last here. There are no clocks and no cooling-off periods, there is nothing to 'cancel out'. You can return on the same day if your rationale supports it. Unlike Schengen, the rules are expressed with vague language by intent so as to give you the opportunity to have a genuine premise and to give them a chance to be flexible ('flexibility' can work for you or against you). The only rule governing this is in Appendix V, 4.2 (b)...

will not live in the UK for extended periods through frequent or successive visits, or make the UK their main home

Adding from comments...

I am not trying to overstay. But Im also realistic that I am better off being with my bf who is in London for medical care for support - than a documented abusive family. I have pysch reports which confirm this - so its not bullsh*t. I really don't have anywhere else to go. And I'm not trying to overstay

That's a secondary agenda which makes a whole lot more sense than your other rationales. Historically, there's been scope for someone with psychiatric problems with no place else to turn and who is reliant on a UK-based person. I had one who got in, got married, had two children, and got British citizenship (then she got divorced and moved back to Seattle). The current era is a whole lot more regressive about these things, but a British Immigration Officer would have no reason to doubt your premise if you could support it adequately. They would still get you on P320 (i), but your credibility would be intact. Since this route is about settlement, you should ask follow-up questions at Expats, we only know about travel.

I really am sick of tooing and froing I have absolutely nothing to hide and perhaps the best way forward is to simply apply for a UK visit visa online and pay the fee - even though as an Aussie I shoudlt have to do that - i read im entitled to come visa free. But given prior YMV, I will do it to ensure clarity about intent. I can forward diagnosis and pending UK appointment for evaluation/treatment. If that doesn work then I give up but I dont see whats wrong with that at all. I really dont

Getting an entry clearance is the SOLID GOLD remedy. You can apply from within the ROI and have an answer in about 5 or 6 days after your biometrics.

And finally.....

also id like to ask what qualifications members of the board have in and to comment officially on behalf of UK Immigration?

Nada. Zero. People on this site are random people on the net who say any random thing that comes to mind. If you get something valuable, it's a random accident. UK Immigration knows about the site because of the referral links in their web stats and the site has the lowest bounce rate of all the social media, but nothing here is 'officially on behalf of UK Immigration'.