That is a very good question, but I don't have any really happy answers. The easiest way to control is to dead-head every day! if you cut or pinch the blossom before it has set seed, there won't be seedlings later.

The next easiest way to control most of the named plants is to hand-pull the extras up as soon as they sprout in the spring, preferably right after a good soaking rain. If you can get them when they are only a couple inches tall, you'll also get the root. You could trowel up the babies and exchange -or give away- at the next plant swap.

A preventive control is to mulch around the desirables, using small gravel near the stem and a lasagna-type mulch elsewhere. Seeds already in the soil -of which there are thousands those plants sent out last year- cannot sprout/grow through the bottommost layer of paper. Lasagna mulch needs to be refreshed each year, just do it *after* the plants have all set and sent out their seed.

Obviously, any extra plants from past years are no longer babies, and a firm hand on the trowel is the most effective way to remove them. Nothing says it has to be *your* hand... with that size garden, consider hiring a young teenager: you pull an example plant (never trust a verbal description!) and then s/he does that actual grubbing. Or, I recall reading about one person who made a bright flour-water-food coloring paint and just dabbed it on all the unwanted plants; helper knew just which ones to pull.

I ditto the mulching. Another way would be to save up them newspapers and when you reapply your mulch this year (if you do) lay down a few sheets between the ground and the mulch top. This will prevent some seeds from doing their work for a few years. Pull out the ones you don't want, and you do have to stay on top of them or they can get frisky. lol

You don't have to dead head every day. lol But once a week (at least) would be a good plan. Take a walk around with a bucket and pick off all the spent blooms before they have time to dry and release their seeds. This should help quite a bit. =)

Mulch well and when you have unwanted plants and don't want to disturb those near by....use Round Up and the "handshake of death". You put a surgical glove on your hand and a cheap cotton glove over that, wet the cotton glove and "shake hands" with the plants you don't want. Be very careful not to get the Round-up on anything you want to save....but this is a safe and easy way to "weed" a garden.
When you are through toss both gloves.
This works well, but you may have to repeat for some plants....and it will take up to 3 weeks for the plants to completely die.
Linda C