single zone hot water baseboard heat... how to reduce heat in "first" room of the series?

You certainly could tee of the supply and return of you baseboard and install a thermostatic valve of some type, either a nonelectric actuator or a conventional zone valve operated through a transformer and a thermostat. This is a somewhat common way to zone individual rooms remote of the boiler room. it can make future service somewhat cumbersome especially if there are a number of these zones spread around a building.

This has actually been thought of over 50 years ago.  On page 21 of this book, Zoning Made Easy I use for teaching a one day seminar on Hydronic heating, is the explanation and a diagram of how to "Zone" a series loop with a bypass.  In this case they used 1/2" pipe for the bypass but if you need the full flow of a 3/4" pipe, that is certainly an option.  By adding insulation to the bypass pipe you ensure that the least amount of heat is allowed out of the convector cover of the baseboard. But too much insulation can be a blockage for the needed air flow what heat is supposed to flow, So use a mininum of insulation there.  There are several ways to add the zone valve. Using the Thermostatic Radiator Valve (TRV) that requires no electric connection works well for the room that overheats by stopping heating in the hot room’s radiator.   In order to get heat in that room there must be  a call for heat from that loop, however when that room reaches the desired temperature set by the TRV, the valve closes and the room stops getting heat while the rest of the zone is allowed to heat based on the call for heat from the thermostat.

Although B&G no longer markets the Thermomate® TRV, there are other companies, like Danfoss and Resideo (Formerly Honeywell) that do offer the TRV you can use for this project. And it will be somewhat less expensive that adding a separate zone with the electrical controls and home run piping to the boiler room that is associates with it.

You just need to find a plumber that can understand what is needed and is willing to do it.

a leak?

If closing the damper and/or covering the fins doesn’t work, you could simply start removing the fins until you get the output where you like it. A pair of tin snips to slice them and needle nose pliers are all that’s needed.

Of course, that’s a one way street that you can’t go back on, so be careful how much you remove.

Yeah I can't imagine adding a bunch of pipe and fittings when reducing convection will do exactly what you want.

The fin tube heats the air via convection, no air passes through then there is no convection, If it were me I would use the regular old aluminum foil in my kitchen to get the job done. This way you are not adding any parts that can fail, and you can adjust it until its about right, I'm assuming if you lived with it for this long you aren't super picky about the exact temp. If you want a thermostat to control your zone then the repipe proposed above would be your best bet, just please leave a note in the mechanical room or something indicating that you have a control valve buried somewhere, it creates confusion when these things are not clear to service techs, may as well leave a not about the foil as well for any future owners.