you say +/- 10%, this means a max. of 20% per step. To have some headroom i suggest steps with 15%.
So the taps are: 0 - 100 - 115 - 132 - 152 - 175 - 201 - 231 input.
You can try to switch with SCR or Triacs. But have in mind not to cross conduct and get a short circuit condition....
Also have in mind the inductive load of the transformer, that means that the SCR does not open on zero cross of mains voltage but on zero cross of transformer current.
This may be up to 80 degrees later - depending on transformer an load.
With these values out put volts are 207 to 253.
253 volts are not good for some products.
Generally out put range should be 200 to 245.
Ideal taps are 0-110-130-155-185-220.(input range 110-240 & output range 200-245 with 4 steps).
For 5 amp current we need 5*110=550+15%=586 watt core.
you say +/- 10%, this means a max. of 20% per step. To have some headroom i suggest steps with 15%.
So the taps are: 0 - 100 - 115 - 132 - 152 - 175 - 201 - 231 input.