[weby]

Note that a 1000 ton ship that is optimized by Spacehips rules(HEDM/Laser rocket) would be more like:
1 armor (streamlined)
1/3 smaller control
1 2/3 rocket engines (3.3g)
9 fuel =450 tons (for 6.3 mps)
8 cargo 400 tons.

So your fuel cost is only $90/ton lifted for the laser rocket and $6750/ton for HEDM and 2730/ton for a spaceplane using Nuclear Thermal Rocket Engines(3 engines so only 330 ton cargo)

As for energy:
1 TJ laser would use 200gw(25% efficiency 1 shot/20 seconds)

Electricity price alternative: one 1mwh at today's spot price is 29,78 eur, and industrial power transfer cost for one random provider is 2.38cents/kwh inclusive industrial power taxes=23,8 eur/mwh so one 6 minute launch you talk about is 1/10 of an hour so 20 000 times those mwh prices =1.07mil euro each=2.14mil eur for 2. So would result in a 4756 eur/ton electricity cost.

It should be noted that you could also make hydrogen cheaper with a on location power plant and electrolysis unit. Basic electrolysis+compression is say 235 MJ/kg ready hydrogen so one of your 10B/200GW reactors would make 0.85 tons/second or 163.4 loads/day and using a 30 day month that is $150 million for 4900 loads or $93 ton fuel cost/ton to orbit.

So if you approve of nuklear drives a NTR seems like a good choice... if you do not like flying nukes but like nuclear plants then laser rocket is your choice, without on site electric supply the price difference to HEDM is pretty low and you lose a lot of flexibility with the laser.

Basically if you allow NTR and use on site electrolysis the cost of orbital travel is trivial(less than long distance air freight today)

As example A space plane like that would cost $95.2mil (3 NTR ram rocket, smaller control, 9 fuel tank, light alloy armor, winged) so at 1.5% it would be $1.428m/month or $47.6k/day or $144/ton if you do one liftoff/day, but at more launches it drops, so you should reach a total cost of <$200/ton with fuel, few launches a day for vehicle cost+loading/unloading costs, crew salaries and such.