My job is building and brazing custom bicycle frames. Been doing it for 20 years now. I'm certainly not a metallurgist, but none of this is very complicated.
To get the complete stem out would require a lot of heat. If I were doing it, I'd try and machine most of it out then heat it up. The smaller and thinner the wall, the easier it will be to get the remaining part and brass/bronze up to temp and get the stem out, without getting the lower as hot. Keeping the desired components as cool as possible is job #1, as every time it hits red hot, it loses strength and is more susceptible to distortion and damage. There will be less of a chance of distorting the lower when trying to get the stem out if the remnants of the old stem are small and take the brunt of the heat.
Bronze brazing rod and brass are the same, with "brass" being used colloquially. It's actually not even true "bronze" but a specific bronze alloy for brazing, with several proprietary alloys.
Silver comes in several alloys, 50n and 56% being the most common. Silver is great for tight fits such as this, as it wets out much more than brass and has a lower melting point. 56% has a slightly lower melting point than 50n and wets out even more. It would be fine for this, as the real strength is in the interference fit, not the braze. Silver costs more, so is used less in an industrial setting. With the lower melting temp, silver allows the steel to keep more of its strength.
Hearth brazing is almost always bronze/brass.
Fillet brazing is almost always bronze/brass, but there are some new silver alloys that will build a fillet.
Bronze/brass and silver use different fluxes. There's both liquid and powder forms.
Bronze/brass doesn't adhere to stainless.
There's a third filler, nickle silver, that will adhere to stainless, stronger than both bronze/brass or silver, and will build a fillet, but it's for more advanced skill levels. The melting point is just below the available flux effective operating temp, so overheating and scorching the flux gets pretty dang easy to do. Turns into a real mess in a heartbeat. The dust is also very irritating to skin and lungs, so it's best saved for special occasions, like high holy days and religious ceremonies.
This is an easy brazing job. Your guy should be able to pull it off with no problem. If he's really on his game, he should be able to get the old stem out and the new one in within the same heat cycle. A cold stem pressed into a hot lower would wipe the old hot brass out, then everything could be heated up, and new brass sweated in.
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