Thanks all for the replies. I found the local (Scottish) building regulations and had a good read through the relevent parts. Then I had to refresh my primary-school trigonomatry and found out that, through pure luck, there is a spot under the turning area at the front of the property which fits all of the criteria in terms of distance from boundaries and buildings. It's possible that we might have to move the house 1 meter back in the plot depending on tolerances, but that is much better than what I had feared.
It was good advice to take a look at recent local planning applications too. I had forgotten that the conversion around the corner, done a couple of years ago, had had a similar issue. While we already knew we were going to have to dig a long trench for our water supply, it hadn't occured to me that we could use the same trench for a pipe to the nearby watercourse (this being what the neighbours did with their conversion instead of using a soakaway).
I have found so far Dan-wood to be good but very slow. It's taken a year of iterating plans to get to something that would work, and I feel like we have pushed the boundaries for them. That said, they have been helpful and patient, proactively honest about timescales, and (assuming it gets through planning) we have a design that we love for a tricky plot without spending thousands on an architect.
And @Bozza you are making me think I have over-budgeted! I remember many years ago being told "a third of the cost for the plot, a third for the groundworks, and a third for the house". We already had the plot (but estimate it would have cost £100-150k with planning), the house is costing about £350k, so I have budgeted £200k for everything else, plus £100k contingency. Here's hoping it comes in at £50k!!!