@davidg12345
The TRO is merely a registration at BCCI in relation to a foreign entity, it's not itself any form of trading thinggie.
Therefore, I'd guess that any address you give is pretty much a correspondence address (to contact you/your TRO) rather than a business address. (But your attorney knows best, if he says it must be some kind of official business service address, then that's what you get. But it doesn't matter where in Bulgaria it is.) Similarly, accountants here might have lots of experience with Bulgarian companies and Bulgarian accounting, but unlikely to do much with TROs.
Pretty much your options with your TRO are to keep putting any business transactions you do through the foreign entity, and/or incorporate a separate Bulgarian entity (e.g. EOOD) to use for some business transactions.
In terms of taking money from your biz, there are 3 main ways: you can be an employee, being paid a salary (with appropriate deductions), or you can be a freelancer (being paid under a service contract), or you can issue a dividend (to the shareholders). All have different tax rules and you'd need to check (e.g. there might be an Australian withholding tax for payments to foreign-based contractors).
I'm not a specialist TRO guy, and it rather depends on exactly what kind of business you're running. But my guess is that you should probably keep using the foreign entity for some transactions. Permanent Residence is 5 years away, and until then you probably need to keep this active and in good standing so you can renew your TRO/D visa.
But it might be a good option to have a local Bulgarian EOOD too. It's worth considering making yourself an employee of the local entity (even at a small-ish salary) so that you're paying your local health insurance contributions. And you can probably expense a bunch of stuff here (company car, company pension, various tech expenses, some travel & entertainment). I'd guess Australia is like UK/USA and has much stricter restrictions on expenses/perks and their tax treatment.
Alternatively, if you're already an employee of the Australian entity, it might be tempting to keep that up. There might be advantages to keeping up your social security payments there and contributing to a pension from a high income country (rather than starting a new one in a low income country). I kept up my UK social security (NI) for some years, as a UK pension is a helluva lot better than a Bulgarian one. Then, in addition, I'd go to my local NAP/NHIF office here, and try to register as unemployed so I can make social security contributions here.
Either way, I'm placing pretty big emphasis on you paying social security in Bulgaria. This is so you have full public healthcare entitlement. Some folks criticize Bulgarian healthcare, but I've had very good experiences with it... and it's way better to have it, than not have it, right? Additionally, most of Bulgaria's private hospitals seem to be affiliated with the public system and get reimbursed by it. There's some bureaucracy involved (in theory) as you should get a referral from your GP that you need treatment X. But, typically, you can get private hospital VIP care, pretty much when you want it, at a ludicrously small private surcharge. I don't know anywhere else that allows this. We have nice private hospitals in the UK too, but if I want something there I have to pay full private list price (i.e. a lot). Having coverage also gets you an EHIC (separate application) which is great when you're travelling/staying in other EU countries.
I pay 20 euros per month, as unemployed. It's an amazing deal. Unfortunately, NHIF is slightly protected from pesky foreigners arriving and wanting an operation. So you, as non-EU, can't register as unemployed immediately. You can either wait 5 years, or you can find yourself a Bulgarian job (either as an employee, or just register as self-employed/freelance). If you're "economically active" they'll register you in the system and accept your contributions. (After an appropriate period, you can stop the work and change your status to unemployed.) Under the freelance option, your contract could be with your existing Australian entity, but you'd definitely need to check the tax situation.
Separately, somewhere along the line for your TRO/D visa/residence permit, you'll need a personal address for all this paperwork. My attorney did a rental contract to keep immigration happy, and it cost me a few hundred euros. Perhaps your attorney can do the same? And maybe he says it's OK for both your address and the TRO address. I did this because I didn't know where I wanted to live, and didn't want to rush into buying/renting something until I was ready... but I still wanted to get the bureaucratic formalities out of the way, ASAP.