Birnie seems to have been from Banff and born in 1760. There's apparently(I've been Googling) a local source referred to as "Imlach" which I don't know but which seems to associate him with Alexander Mackintosh whose daughter he is said to have married. Electric Scotland is looked after by the Clan Fraser Society of Canada, which has very good genealogists. He must have had a fairly long association with Mackintosh if the partnership was dissolved in 1802. I'll see whether I can dig anything up from what I have here, but I don't think I have much that would help. Prinny's order seems to be the sort of thing that would crop up in a Birnie obituary, quite possibly based on stories he would have told to his friends.
There are two accessible sources for wills. A Scot with a Scottish estate who made a testament would have the will proved posthumously at the local commissary court and the will would then be recorded in full by the court. Not many made testaments. The surviving records are accessible through the Scotlandspeople website, which is tricky to operate and works on a system of pre-purchased credits, but will track both names and places within date limitations of your choice. The will itself, when you get it, is quite expensive -£5. The Registrar General for Scotland subcontracted the management to a subsidiary of DC Thomson, the publishers of the Dandy and the Beano, and their customer service is not the best, but their contract is apparently moving towards its expiry date. What is actually in the document might vary widely. The most common result is an inventory, not so much of real property as of debts, owed and owing. Family information is far from invariably present, though if it is it will be detailed. The more prominent the testator, the more likely it is to be detailed.
Many American and West Indian Scots who made wills tended to have them processed in their place of residence at death if their estate was wholly there too, which means, for example, that many West Indian wills, if they have not deteriorated from bad storage conditions, have to be consulted on the spot. If any British property or legatees furth of Scotland were affected, they were proved in the Prerogative Court of Canterbury and will have progressed to the PRO, now the National Archives, at Kew. Their holdings can be searched online, and once you get used to it, the system is easier to operate than the Scots one, though there are pitfalls - the initial search is within 50 year time bands, for example, though there is an advanced search which, if you are fairly sure about dates and places, can cut down the sorting of the results, and it is not a good idea to enter both forename and surname - you get very large numbers of hits if you do, which take a great deal of going through. A surname is usually enough if you know the rough date of death and likely place. You pay nothing until you order, and the rate is £3.50 per will (but of course they have a larger clientele). A very good zoom function is a great help. The copy clerks were only human, and it's sometimes very hard to be certain about names if they were tired or overloaded.
I note the list of Ewen's children. Alexander Clark's will - 1810 - mentions a male child then unchristened, and he doesn't seem to fit with the list. Do you think others might have been christened elsewhere?
I think perhaps I should try to send you James Clark's will, which confirms the relationship between Dr Anderson and Robert Anderson the Inverness silversmith (but not much else, though it's a fascinating document if you are interested in fine art and the way the Italian-Grand Tour market in Greek/Etruscan vases worked at the end of the eighteenth century - Alexander doesn't seem interested in that sort of thing, apart from his nine volume book on Herculaneum). I'll do so when I have checked I actually have all of it. There's an incomplete draft in the National Archives of Scotland - and even this one wasn't accepted as wholly authentic by the PCC - they thought the original, in Naples, would be needed for more than a grant of administration! I don't have notes on them here, but there are some James Clark letters in the NAS which I seem dimly to recall are from 1792, when he was in England, and may mention things which might be happening in Haymarket around the time of James's birth. I'll get my notes on them to you when I can.