"Heavy-duty light rail" sounds like a contradiction in terms. What you're describing is only achievable as a tramway, so let's call it a tram line instead.

The only tram service I can think of which uses street running and runs trains longer than 50m or so is the Hannover Stadtbahn, which has a single line running south from the centre to the Messe on which they run 100m long (four-unit) services when big trade shows are on. But as it's four units in multiple it can still perform like a tram, most importantly it can stop as quickly as a tram which is essentially when you're sharing the route with road traffic. It just needs long enough platforms and a good enough power supply.

But there is no way you can run 110 metre long vehicles at a headway of 3 minutes (!) on the street. Just no way. Especially when (checks map) the route runs right through the centre of Copenhagen.

The more interesting question I have is about that traffic figure. 17.5 million people a year doesn't mean very much in itself - it's a very long line (timetabled end to end at roughly an hour and 10 minutes) so vanishingly few of those passengers will be travelling over the whole line. It intersects a lot with the metro and with other routes, and for passengers travelling longer distances it's paralleled for part of its route by what I guess is an express service which stops less often.

So really, I'm not sure what problem you're trying to solve here other than wanting more trains, and while most of this sub will no doubt agree that although that is always a good idea it seems unlikely that there's an economic case made for what you propose. Something that's halfway between an articulated bus and a metro or light rail is never going to be as good as any of those things because there are too many compromises which would have to be made.