One solution is to keep your present brifters and find an old pair of downtube friction shifters (and a clamp with bosses) so you can shift the triple.
Added advantage is if your rear brifter fails you have a back up.
A single front bar-end shifter would work too if you can find a second hand one
When I built up my rando bike in early 2016, I had a rear brifter but no shifter for the front. As a temporary measure I put on a vintage front friction shifter (Huret). Then started thinking about what front shifter to install for permanent use. That was nine years ago.
That front shifter is still in use, no longer considered temporary.
I had to use a file on the cable fitting to fit it in the shifter, they used different fittings on cables half a century ago.
There is a plus side to using a friction front shifter with a triple crank, if you have an indexed front shifter and a mis-matched front derailleur, it can be difficult to get the shifter to work just right for shifting onto the middle chainring. But a friction (unindexed) shifter has no problem with that. Eventually you develop muscle memory to be able to shift smoothly to the middle chain ring.
For a year or maybe two Lance Armstrong used a friction front shifter on his racing bikes instead of a brifter.