What makes them 'upside-down'
And did you refit the cup washer below the top mount (cup face down - opposite to the top one)? Not doing so will blow the top mount in pretty short order.
Also have Bilstein improved the rear fitting kits? Always found them underwhelming compared to the Sachs/OE fittings Rear shock upper threads were nearly an inch shorter than the Sachs/Factory ones.
So called "upside-down" Bilstein front dampers have the body containing the oil in a large diameter chamber that looks like a massive piston rod at the top of the shock, and the rod then is screwed to the bottom of the strut. There are benefits in unsprung mass (marginal) and rigidity (mainly) when used in a McPherson strut where bending loads are applied to the assembly. They were popular for use in rally applications for this reason.
The struts I acquired were new old stock, and the rears were the last ones in the country. You are right there wasn't much in the way of a fitting kit, but fortunately all the Lotus Carlton stuff we have in stock is compatible, so we fitted new Peddars uprated top mounts and our S514 Lotus spec cup washers to the top, and had some new bottom bolts and GSi top mounts for the rear.
Car is noticeably firmer now (only just on the acceptable side of uncomfortable), which is compounded by a switch to 17" Alloys with Nangkang cup tyres all around that replaced the 15" ancient Goodyears that it came on. On a previous car I did a back to back and the Nankangs were firmer than Uniroyals, so I left the Uniroyals on the comfort barge that I have now sold.
Plan is to fit the LSD next, and better front brakes before converting to manual box and lighter flywheel next year.