My advice is to do this yourself not only to save money but also to turn that frustrated feeling you have from all those leaks into pride for making the job right. Don't just fix the leaks but redo the whole thing and start from the vertical line seen in your second image (I assume that's your supply).
If the horizontal lines in both images connect then dig down 8-10" and run a line from your supply straight over to your BFP so that the horizontal line will be underground. Place the BFP on the ground and enclose it in an irrigation box (Plastic UGV). This way the only exposed plumbing will be a vertical line coming up then one 90 deg turn in through your wall. I would also trace that pipe back through the wall (hopefully it's exposed, crawl space perhaps) then cut back to the first convenient spot where the pipe is clean and run new stuff back out. If you put a gate valve on the new vertical line you can shut off the supply to your house to do plumbing inside and still have accessible water from an outside faucet (to put out the fire from your torch). Make sure any outside faucets are past your BFP or use an anti-siphon valve, from what I see in your second image it's possible to get a siphon with a hose attached to that valve. I think doing all that would be worth $700.
Copper to galvanized steel will cause electrolysis and quickly corrode the metals, you have just made a little battery, so use like metals (copper/brass) but if your house plumbing is steel you can connect copper to it with a dielectric coupling.
When you are soldering copper make sure you heat all around the connections, you can get a break in the solder, causing a leak, due to a cold spot. Water in the old line can also cause cold spots, copper conducts heat fast and steam will actually cool the metal. For this I use good ole' white bread, no crust or seeds, roll it up making a half inch plug and push it in the pipe with a pencil. This will hold back the water long enough to finish the job and you can easily flush it out a faucet that does not have a screen, like your bath tub, just make sure to leave that valve open and all others closed before you turn on the water. There is a product you can buy for this purpose but wounder bread is cheaper and much more fun.
The way I learned how to plumb was to do a job (wrong) and then chase down all the leaks, getting frustrating I would redo it all but this time do it right. A clean professional looking job changes all that frustration into satisfaction and makes it well worth the time. You know....I think it's much more fun talking about plumbing then actually doing it, especially if there are spiders in your crawl space.