You DO need a slate repair because a PROPER tie-in from the lower asphalt shingles to the existing slate would be that the slate overlaps the asphalt shingles approximately 18" (preferrably closer to 36"), so there is no way to PROPERLY make the repair without removing at least the first course of slate, installing the shingles, and reinstalling the courses of slate. This CAN be done, but if you don't want your slate roof touched, it can't be done PROPERLY.
Heck, a proper repair would be to remove the asphalt shingle and re-install slate. That's why I said the repair in the past was improper. Whoever would have done that to your roof was just out to make a buck.
As for "lucrative", I (as all
professional contractors) price every job to make money. Making money is not a sin. I'll go out and repalce 1 shingle or caulk 1 chimney, but I will make money on every job. Every job can be lucrtivate assuming the customer is willing to pay a fair price and isn't asking for charity.
Anything CAN be done, we put a man on the moon, just remember that costs billions of dollars. So yes anything can be done, if the budget allows. In other words anything is possible, it just costs more. Also remember there is always a right way and a wrong way to do things.
If a slate roofer from Holland or England were to see that asphalt shingle installed with the slate, he would likley fly back tot he old country cursing all Americans for their lously workmanship. The slate roofing teqhniques are available for all who take a moment to educate themselves. For example I have the Slate Roofing Bible as well as the National Roofing Contractors Association's Roofing Mauals. The information is out there on how to properly install a roof. As I said I am no slate expert, I've only installed a couple of slate roofs. I would reocmmend seeking out Tinner who does much more slate work than I or English Roofer from
www.roofingtalk.com I do suspect both are going to tell you that there is no proper way of doing it without removing at least some slate.