Any tricks people use to seed large areas without inground irrigation systems?
I don't know that there would be any trick per se. Ultimately, there's a certain amount of water you need to get onto the lawn, and it takes a certain amount of work to accomplish that.
You're already doing the easiest thing: pick the right time to seed. Early spring or early fall gives you a better chance of natural watering, without excessive heat to dehydrate the soil. The downside though is that grass seed needs a certain minimum temperature to germinate, and so you're dependent on Mother Nature to provide the water without also making it too cold. I don't know for sure the climate where you are, but I'd guess Western MA tends to stay cooler in the spring, and starts to get cool earlier in the fall, making this timing tricky.
But to the extent that you can manage timing the natural water and temperature correctly, that's the best "trick" you can come up with. The modern era of climate change is going to make this a lot more difficult in many regions, but the key is to pay attention to the weather forecast (which is reasonably accurate now up to even two weeks out, at least as far as planting goes) and "strike while the iron's hot", so to speak.
That said, I would say that you're not making things exactly easy on yourself with the rotary sprinklers. These have to sit out in the lawn, creating extra work for you when you have to mow, never mind the fact that you really don't want to just leave the sprinkler and connected hose laying on the grass when you're not actually watering, lest it kill the grass under it.
Instead, consider using a "fan" oscillating sprinkler, or even better an impact/pulsating sprinkler. The oscillating sprinkler is convenient because it can provide a relatively uniform width of coverage of water, almost rectangular in shape. An impact sprinkler provides a circular arc of coverage, which is harder to arrange evenly, but one nice thing about them is that you can get them with a tripod mount, elevating them out of the way of the mower.
In either case, they can be set up on the edge of the lawn, away from where the mower will be. You still need to run hoses out to them, which preferably you could do without crossing the lawn itself. You could even consider adding spigots to the landscape — a matter of running some PVC pipe underground, connected to the water supply on one end and putting on a regular hose spigot on the other hand. It's more work than not installing irrigation at all, but less work that a full-fledged irrigation system, and more flexible for other watering needs.
If you arrange things correctly, you essentially wind up with an irrigation system, but with significantly less effort and cost to install than a real irrigation system would be. Importantly, done right you would have sprinklers set up that you could leave set up even when you have to mow (just be careful mowing around the edges).
Now, you do mention this:
Seeds are costly but time would be saved, if germination is at least half decent.
Naturally, if you're willing to trade cost for time, one option is to go ahead and hire someone to install an irrigation system. Expensive, but it can be done in a way to completely solve your grass irrigation issues.
Alternatively, you could spend the money on a gardener/landscaper who will handle the lawn watering for you, i.e. deal with the hassle of moving the sprinklers when the water needs watering and when it's done, so they aren't in the way when the mowing has to happen. And of course, you could pay them to do the mowing too. :)
The irrigation system has a higher up-front cost, but would probably cost less in the long run. It will have on-going costs, because things will break and need to be fixed, and of course it will need to be blown out every fall to ensure against freezing over the winter. But those on-going costs would probably be lower than the labor costs for the watering and mowing long-term.