An SSR is probably the optimum part to use. Assuming your AC is 50Hz or 60Hz, each cycle lasts 20mS or less so if you turn it on and off 10 times per second, you have no more than 50% of one tenth of the time to enable the power, that only gives you a few mS in each burst. If you use a mechanical switch, whether reed or conventional relay, the time taken for the contacts to move will be significant and cause a large loss.
You might be able to use opto-MOSFET switches as an alternative but I'm not sure you can get ones that can switch such high voltages. Possibly using the two in parallel will work, the MOSFET ensuring low loss at low voltages and the SSR doing all the hard work at higher voltages.
Don't forgret you can make your own SSR from a pair of SCR's and an opto-coupler, it might be cheaper than a ready made unit.
Brian.