The power supply you show I think is rated 35 - 105 VA which I always questioned when used with mutli-lamps as really at 10W each it should have been rated 10 - 105 so it would continue to work with only one bulb still intact, it was designed to run 4 to 10 x 10W bulbs, as it states the transformer device can be dimmed and it also correctly states you should not dim halogen lamps specially that small, the whole idea of a halogen lamp is the envelope is so hot that the tungsten from the filament will not be deposited on the envelope but instead back onto the filament, over time the tungsten will not be re-deposited in an even manor so it will develop thin and thick bits and in the end the thin bit will rupture. If the lamp is not kept hot enough you will see the quartz envelope go black inside.
At 1 to 2 watt each maximum wattage would be around the 20 watt mark which is too low for that transformer, and at around £2.30 each 10 would cost around £23 plus new transformer at say £6 so it would cost in the region of £30 to convert to LED.
However you also state main lights are G9 these should also not be dimmed, as quartz lamps, so option is to change all to LED with new transformer or get rid if the dimming.
As stated 300 watt is a fair amount of heat, likely OK in the winter, in fact likely will if heating is all electric reduce the heating bill because inferred heating does not heat the air directly so you can reduce air temperature to 18°C but the room will feel as if air is at 20°C but 300 watt is over 1A and unlikely you can find a dimmer to take that load at a reasonable cost and also in the main we use ceiling roses as junction boxes which are rated at 6 amp so the fuse/MCB/RCBO for lights is just 6 amp, and likely for the whole house. So you need to consider if you have a large enough supply.
In the summer you may want the ability to switch off some of the lights, so consideration must be made as to if the lights should be split into two circuits, this is common in Europe so in your case you could have 100W or 200W or 300W with just two switches, you would not really need a dimming switch if set up like that.
I think the whole idea of heating with lights may be more economic, that is something which can be debated, but 15 quartz bulbs in one room would be high maintenance, every week you would be renewing bulbs, and in the end you will be forced to swap anyway as the supply of quartz bulbs is phased out, it is a lot of work to fit those lamps correctly and build or fit the fire proof boxes or hoods around each lamp, unless of course on the top floor, so personally I would not fit them.
I fitted pods in my bathroom, got them cheap, thought they looked good, but rarely were all four working, one bulb at least also seemed to be out so did not really look that good, I was lucky powered with a proper wire wound transformer I have been able to move to LED, in fact most of the house now LED, that has resulted in near maintenance free lighting, and also released a cupboard which was used to store replacement bulbs.
In the last year I have replaced just one lamp, a 6 foot fluorescent in kitchen, and when I came to replace it seemed it was simply disconnected and really did not need a new tube, pre LED I would replace around 100 bulbs a year, a task I am pleased to have lost.
