You cannot control an AC powered heater without on/off pulsing. The AC voltage and current go to zero 120 times a second (in the USA), which means at those points the element is off. Phase angle power control, is still on/off switching, but at a cycle time of 8.33 msec. So, everything discussed so far in this thread is still on/off pulsing. The only thing changing is the cycle time, which for the options discussed varies from 8.33 msec up to 2 sec.
The only way to get zero on/off pulsing is to use a controlled output voltage DC power supply. If you want to go this way, a switching power supply is much more efficient than a linear supply (I don't even know if you can find a linear supply at ~5500W.)
Looking for a solution implies that there is a problem that needs to be solved. Many of the replies to this thread are asking what is the actual problem that needs to be solved, and noting that there is no real unsolved problem related to powering heating elements in homebrewing applications. One of the basic tenants of engineering is that if you don't understand and state the problem correctly, you are very unlikely to find a good solution.
Brew on