Disclaimer - I am a long term ex-UK expat, not a tax lawyer.
I have always found the IR to be reasonable and helpeful. Personal experiences do vary. Maybe it's cause I earn so little they don't feel the need to grab at it too hard?
Just because you are resident in another country does not mean you will be able to be non-resident in UK. You can be resident for tax purposes in more than one country. So the main thrust will need to be to become non-resident for tax purposes. Even that might not help you though.
What being non-resident for tax purposes will exempt you from is UK tax on non-UK earnings. It will not exempt you from UK tax on earnings 'arising in the UK'. Your only source of relief beyond normal threshold stuff is double taxation treaties.
See this page, questions 3 and 6:
http://www.hmrc.gov.uk/cnr/faqs_general.htm
If / when you establish non-resident status for tax purposes, the key issue is if your earnings are considered to arise in the UK. I would think if your company has its headquarters in UK, flies mainly from UK, and you are paid in UK, then the IR (or HMRC as they are now known) will consider your earnings as arising in UK and tax them as such regardless of residence. I think this has arisen before, and been dealt with in the courts.
Any chance your company has a base outside UK at which you can belong?
I'd be interested to know if anything your accountant says differs from what I have written - these things do change and I might be mistaken or have missunderstood the rules.
Best of Luck!