We are flying in F on our next flight so I'm wondering if the FA's might try to find closet or overhead space for them? Eclipsepearl, what are your thoughts on bringing the seats on board and stowing them?

That sounds reasonable, especially in F. Pack the high back portion well in your bags, surrounded by soft clothes, preferably in a hard-sided suitcase. I wouldn't buy one especially but perhaps you are taking one anyway...

The point is that if your bags don't make your flight somehow, it's not a big deal if the kids are in the booster without the back for a day or two until they're delivered.

If they are Graco Turbo boosters, there's a small black strap with a red plasitc clip, that comes with the Turbo Booster, to help guide the seat belt. You may want to take this along (small, not a big deal to take) and look at your manual. This would make it a better fit, especially for your 4 year old. I still use that for my almost-7 year old, who is bigger than average but has a short torso.

Also, consider the car you'll be using. I found that the high back was less comfortable in my husband's Lexus. Depending on how much driving you'll be doing, you may want to leave either/both at home and just bring the bottom.