I had 5As at Higher (maths, physics, chemistry, English and French). I got unconditional offers for MEng Mech Engineering at Strathclyde, Glasgow and Edinburgh last year so you'll probably be OK (although I was widening access as low progression school, not sure if or how much that contributed). I can't remember having to submit predicted grades for S6 subject which is just as well as got As for my two crash highers but my two AH were poor. But they were still worth studying as a lot of the maths and physics has been repeated in my first semsester this year.
Friends who got conditional offers (not just for engineering) were asked to get either another A at Higher or B at AH. Offers for me came through from Glasgow and Edinburgh in mid Jan and mid Feb respectively, but Strathclyde wasn't until mid March. So you really need to keep the studying up until you know your offer.
Remember you can apply for BEng at both Glasgow and Strathclyde and move to MEng if you have the grades in 2/3rd year of uni. Also if you start in MEng and don't keep up the grades you will be moved to BEng. I applied for MENG, but as I was very keen to go to Strathclyde I also applied to Strathclyde Engineering Academy as a back up incase I didnt get the offer I really wanted (got offer for that in December). The engineering academy is an enhanced HNC and if you pass you get direct entry to 2nd year BEng, then you can move to MEng if you get the grades. I spoke to a Unibuddy student who was on the last year of his MEng via that path and recommended it as an option based on their experience.