Removing Paint from Concrete, Masonry, Limestone

I have a hard time sitting still without getting antsy. I think it's because I work for myself, so time spent not working on a project is time spent not making any money. When I'm not on the computer, I feel I should still be doing something somewhat useful and not just sitting around and relaxing. Ted's much the same way.

A few days ago, when the weather was in the sixties, I whined until I got Mom and Ted to sit with me on the front steps to enjoy a cup of coffee and watch the world go by. The picture below was taken in winter, but that's pretty much what the front entrance looks like now, just without snow.

But did any of us sit still? No. I'm pacing back and forth in front of the house, coffee in hand, discussing plans for the garden with Mom. Ted was sitting on the porch in the shade, but in between sips of coffee he's working on this:

Scraping off flaky white paint. (What's the matter with us? Why can't we just relax?)

The previous owners had coated everything they could in white paint prior to selling. The interior walls had a fresh coat and I think the same paint--interior paint--was used to paint over all of the decorative masonry on the exterior. If you look at the top photo, you can see that all of the window sills and all of the horizontal trim has been painted white.

You can tell better in this photo (from the original listing):

So those little squares at the top, those long horizontal decorative bits that wrap around the house, and every window sill has been painted white.

Only, I'm pretty sure it's the same interior paint used on the walls. The flat surfaces are mostly peeling and flaking, and I don't recall them doing that last fall when we first saw the place. Winter was harsh on them. It's very easy to get the paint off these surfaces with a scraper, and as Ted removed the paint, we saw that the surfaces are actually dirty, and in some spots there is green algae, or whatever it is that grows on limestone. So the paint doesn't have a firm grip. At least not on the horizontals.

Ted made some decent progress that day, and every nice day we've had since I've been out there with my cup of coffee. I have most of the flat surfaces by the front steps now clear of paint. But I still have the vertical surfaces to do, and I'm encountering quite a bit of trouble. The stuff is not flaking nearly as much, and in some parts, it's quite stubborn. I'm afraid of scraping too hard.

I was hoping not to have to go the chemical route, but I think a trip to Sherwin Williams or Home Depot might be in order. I had tried a soy-based paint remover on some of the interior brickwork, but without success. Although I've heard a few good things about PeelAway 7 and its use on masonry, I haven't personally encountered anyone who has tried it for such. I tried PeelAway 6 on some woodwork with mixed success--it's okay on latex, but has problems with enamel. Is there really that big a difference between the 6 & 7? I haven't been able to locate the PA7 locally, and it's pretty expensive online, so I'd like to know more about it before making the investment.

So, does anyone have a recommendation for removing paint on masonry? Have you been able to remove paint from similar surfaces?

Update: My apologies to Dynochick; I originally called all of the decorative trim concrete, when it fact some if not all is probably limestone. I was not aware of just how different the care of both materials are, and carelessly mixed terms. Sorry that my post led you astray.

Before heading out to the paint store for PeelAway7, I decided to check for some coupons online and found one on another blog for 20% off at Sherwin Williams. I'll give it a try this week. Hope it's a valid one.