Gleneagles is beautiful, I can see why you would want your wedding there, but the cost is high and to avoid the embarrassment of all, it must ultimately be your cost. Like others have said, the venue attracts people who have no issue buying the full package - and they can choose the weddings they host - this rule helps them to stay exclusive,
I'm sure you've looked at these, but here are a few suggestions - not all meet your spec
Hopetoun House, Dundas, Carlowrie (beautiful-just opened so still exclusive on the wedding scene), Orocco Pier (stunning views - very good at weddings), Norton House Hotel, Cameron House, Mansfield Traquir, George Hotel, The Carlton (stunning refurb). There are many places in Fife too
Reading the thread, I'd suggest that exclusive hire would suit you more and achieve the country weekend feeling your looking for.
Also, fwiw, although I don't regret the £££ we spent on our wedding, on reflection we could have spent half and it would have been as special - weddings spiral out of control - stick to you original budget. Focus on your guests and role as a host and keep Gleneagles as your weekend away treat.
Have a fantastic wedding, your day will be perfect for you, whatever you choose