You guys are going about disassembly the hard way. Take a note of the pressure regulator. It is a coupling type. That means it can be disconnected and removed without de-soldering anything. See the coupling portion on each end of the pressure regulator? It helps in dismantling – so I would recommend replacing it with same type, same manufacturer if possible (which will keep the dimensions the same and would be able to reuse the upper coupling connector and elbow w/out dismantling that). Note that the gate valve is before the pressure regulator – this is to allow easy servicing of the pressure regulator.
Turn off water at the street connection (meter), I tend to drain by opening one of the highest faucets and most of the lowest. Even after draining, you may have quite a bit of water coming out of the line after the regulator (pressure regulators also act like a one way valve). Be prepared – water draining is unavoidable and can be a surprise when a kid or spouse decides to try a faucet upstairs even after you tell them the water is off – it happens.
After removing the pressure regulator, the lower end with the gate valve will be easy to remove (comparatively). Water feed is from the bottom, and you will need to remove water from the lower portion, probably by siphoning. Even with MAPP gas, water in the pipe can make it hard to heat because water can absorb a considerable amount of energy and copper is a great thermal conductor. Just work towards the ends when the regulator is removed. No cutting needed.
Important
If the pressure regulator is still working (check with a gauge – make sure you are measuring after the regulator because some outside/garden lines are fed pre-regulator), you might not want to bother touching it – check for pressure creep with all lines closed. Your regulator is adjustable. If it turns out that your gate valve is the only thing not working right, you may want to consider fixing it. It looks like yours may be the ‘serviceable’ type where you can remove the gate and stem without removing the valve body. The main problem with gate valves is crap getting into the gate channel and preventing it from closing completely. Gate valves do not seal/close with a rubber seal – the only rubber washers are on the stem. Gate valves use a tapered brass ‘gate’ – thereby the name. Closing the valve drives the brass gate in between two tapered brass seats (like a wedge). The second problem occurs when people don’t open them all the way, and water passing through wears down the edge of the gate over time. Gate valves should be all the way open or all the way closed – never ‘between’.
To remove the gate assembly, just open the gate valve at least half way, remove handle, remove packing/seal bolt (nut closest to handle), then loosen at the next nut which is part of the top of the body (there is a seam line that is sometimes hard to see – you’ll see it when loosening). You may need to jockey moving the gate by turning the stem vs turning the removable portion of the body. NOTE: Do all the above after turning off water at meter and draining.
When I re-pressure, I tend to crack several valves located at the high point in the house and then crack open the street/meter feed. I then start closing off the house valves as water starts flowing smoothly. When all house valves are closed, I open the street all the way.
NOTE: MAPP gas is the only way to go with this one. You may be there until eternity arrives with Propane.