I've got a 10kva 3cylinder lister diesel geny and it runs my 250a mig and my 250a stick without problem. You can hear it load up but that's what it should do.
AREP (Leroy Somer's name for an Auxiliary Winding) and PMG's are very much still in use and common.Many years ago, we used quite a few generators to run gas extraction plant on landfill sites. The gas booster that sucked the gas out of the site had a 3-phase 7.5 kW motor with direct-On-Line starting. DOL starting draws around 6-7 times the Full-Load Current on starting. We used an assortment of generator sizes, depending on whether or not they had "improved excitation".
With improved excitation, we could start and run on a 27 kVA generator with no problem at all and, in a pinch, could get away with a 22 kVA. We tended to use generators hired from a company that supplied generators for use with pumps and they all had improved excitation. When we had to get in generators at short notice from other suppliers, they usually came without improved excitation. We had serious trouble starting on 60 kVA generators on a number of occasions, needing to switch the gas booster selector switch to "on" and then start the generator. It was hard on everything, but was the only way we could get the booster started.
Without improved excitation, the generator slows down under the starting load. As it slows down, the Voltage reduces and things spiral down until something fails.
The improved excitation usually consisted of a Permanent Magnet Group and Automatic Voltage Regulator on the excitation circuit that effectively removed the link between excitation Voltage and speed. There was also another improved excitation system, AREP, that was fairly new at the time (late 1980s, early 1990s) and worked differently to achieve a similar overall effect to the PMG and AVR.
It is probably worth noting that the PMG and AVR were on the excitation Voltage, not the output Voltage. I don't know whether a generator that includes "AVR" in it's description will have improved excitation, but I suspect that the Automatic Voltage Regulation referred to is likely to be on the output Voltage only.
The best thing to do is to talk to a good generator supplier (or three), explain what you need to do and ask them what they can offer. You may find a generator rated at half the output with improved excitation will do what you need. If so, it is likely to be cheaper to buy (even with the added cost of the improved excitation) and considerably cheaper to run.
PMG though was very common for UPS & Inverter loads (& for 3ph sensing) more than motor starting.
On industrial 4-pole alternators these days, an Aux Winding design is pretty much the standard. Only very cheap stuff might be a shunt excited unit nowadays.
(Shunt excited don't have any overload capability for transient loads like motor starts, where the above can accept up to 300% overload (over-current) for something like 5-seconds).