Wow!
1 -- The best options for one child over 40lbs are all terrains (Mountain Buggy, ABC, Valco) because they have higher weight limits and still steer well with one heavy child and one light child. Depending on your son's maturity, you might also be able to use a single and a board (if he'll stay on it--my 3.5 year old only JUST gets the concept, and not very well at that!) Because of the higher weight limit on Maclarens, you could also try a Twin Techno but they don't steer as well with uneven weights (pull a bit to the side..) (Don't worry about the weight limit on it as long as it continues to feel stable--a couple of stroller manufacturers have recently admitted the weight limits are guidelines...unlike carseat weight limits!)
2 -- The Runabout IS heavy/wide. I hated mine. I would suggest an ABC double with a toddler seat if she wants to go "compact" and can afford it.. I suppose if any one of the children are mature enough, she could also use a nice double and a board (there's one that has a seat on the board, for example..) Mountain buggy's triple folds up flat and fits into the back of a minivan, but it's still a beast

Oh--you know what also might work (depending on the kids)...piling them all into a Chariot double, if you don't need to get through smaller doorways (you still CAN--taking one wheel off.) My neighbours and I sometimes pile our three 1-2 year olds into the Chariot together when we do school pickup. It does mean one won't be harnessed if that's an issue (you do what you've got to do.)
3 -- The triple Sit 'n Stand would work if she was keeping it up in a garage and loading the kids in. She could also do a double with a board, or a double jogger with the wrist strap for the 5 year old to hold onto (works GREAT for older kids who're walking next to the stroller)... For *inexpensive* double, the most inexpensive double that's still a good quality stroller would be Kolcraft.. It's no Maclaren or Inglesina but I think it runs about $60 and as long as she's not over about 5'7" should do the trick. I suppose she could even rig a strap to that--when I worked in daycare we used to take the 3-5 year olds out with a big long rope and knots tied at intervals for them to hold onto. It was never a problem. (Having a three year old that bounces off walls now, I'm SHOCKED it was so easy in daycare!)
4 -- Does the six year old need to be in a stroller, or better yet--can the six year old PUSH the four year old or one of the triplets? That might be an option--pick up a Maclaren Volo (easiest to steer) and give the six year old a job. It slips into a minivan trunk behind even a triple Mountain Buggy with room to spare. I often have my 8 year old pushing my 1 year old in her Cameleon to keep him busy. I have four kids (naw, we're not going to try for a 5th, heehee) and I've learned that delegating is the only way to remain sane!
-N.