Bob (Iwire) was on to something when He mentioned the duration of time the Toaster will be on / off.
Simply, this equates to the "LCL thingee" we all know and respect
The "# Amps × 1.25" adder for Long, Continuous Loads
is of design interest for this situation.
If the Toaster is on - and drawing full load current of 28.5 Amperes @ 208 VAC for 179 minutes, then is turned off for a brief period of time, this is not an LCL - as it falls just one minute shy of the 180 minute mark.
If the Toaster _DOES_ run at full load amperage of 28.5 Amperes @ 208 VAC for 180 minutes _OR MORE_, then it is an LCL - requiring an additional 25% of circuit ampacity rating (even though the appliance does not draw that additional 25% load current).
It's not a bad design idea to use a 35 or 40 Amp 208 VAC 1Ø circuit, since the Toaster is so close to the 30 Amp point - and it's a Resistance load which may tend to draw a higher load current as the system voltage increases (and vise-versa, decreasing load current as the system voltage becomes lower).
The 30 Amp cord might be an issue in more ways than simply insufficent ampacity - duty, enviroment, heat tolerance, etc. should be considered as well.
Here are some simple calcs, compiled from the listed values of the equipment and system:
Mfg. listed FLA: 27 Amperes @ 208 VAC 1Ø
w/ LCL = 33.75 Amps (27 × 1.25).
35 Amp circuit minimum.
Running Amps: 28.5 Amperes (was this measured by you while the appliance was running?).
w/LCL = 35.625 Amps. Looks like 40 Amp circuit minimum.
Using the FLA values of 27 and 28.5 Amps @ 208 VAC, it appears the Toaster has a total Resistance of 7.5 Ohms (7.3 Ohms for 28.5 amps, 7.7 Ohms for 27 amps @ 208 VAC).
If the system voltage is right at the "Target Value" of 208 VAC, the FLA will equal 27.73 Amperes @ 208 VAC.
I saw that you measured an unloaded circuit voltage of 205 VAC and a loaded circuit voltage of 200 VAC.
With these values applied to a 7.5 Ohm element, the FLA values would be:
FLA at 205 VAC: 27.334 Amperes (5603.47 Watts),
FLA at 200 VAC: 26.667 Amperes (5333.4 Watts)
and just for fun, if the voltage rises to 215 VAC, the FLA through a 7.5 Ohm element would be:
FLA at 215 VAC: 28.667 Amperes (6163.40 Watts).
Hopefully this message is one of the following:
[*] Just what you needed,
[*] A little help, or
[*] Very entertaining - mainly from silly content!
Let us know what the LCL standings are, and the measured values of Amperes @ X Volts.