I hear you, cerdaclan! I have the same worries about my 7yo.
Last year we stopped using Singapore Math 3A--which was requiring a lot of time because he didn't know his times tables yet, and still doesn't. But like your DD, he understood the concept of multiplication and could work lengthy problems without difficulty. He was just s-l-o-w-w-w-w! But he was hating math, and I wasn't okay with that.
We shifted gears to geometry, and that went swimmingly. And not that "this is a triangle" stuff that passes for elementary school geometry. Real geomery, albeit light on proofs. (But still heavy on logic and critical thinking.) It was challenging enough conceptually, but light enough on arithmetic, that he was in math heaven!
This year we're going to do some Living Math in a homeschooling coop, I think, so more geometry stuff. Plus we'll do some physics and calculus at home, at least conceptually. (DH is an engineer, thank goodness!) All of this should bring him to algebra in some fashion, which I expect to use in part to help him learn his times tables.
I realize that our approach seems backwards--"Calc before times tables! She's crazy!"
But I decided we should proceed according to where DS7 is conceptually rather than letting arithmetic hold him back. I figure most kids have to know their times tables by, what? 9 or 10yo? So that's when my son has to know them, too. But if he's ready for higher math concepts before then, then he should get them. We'll just find workarounds, much as you are doing.
A lot of HG+ kids only learn their times tables when they hit algebra. It's common. My goal is for my son to love math first, and to progress second (since the progress is really the easy part with him). I figure he's a good bit ahead in math, and it isn't a race, so there's no need to rush him to memorize math facts, especially if that has an overall negative effect on how he feel about math. Love first, progress second, and I think that way we'll actually get both love AND progress.
They only have to make a year of progress for a year's worth of work. More is swell (and is likely, with these kids!), but is not strictly necessary.
Oh, and if you let her use the calculator, you might consider having her multiply each digit one at a time. In other words, instead of typing in 5832 x 6789, have her type 9 x 2, then 9 x 3, then 9 x 8, etc. That way she a) gets to see the facts more often, and b) finds using the calculator to be a bit of a pain, so she may decide it's just easier to memorize the tables. Just a thought...
I'm interested to hear more about what you're doing, since it sounds like we're in something of the same pickle!
