An experienced contractor could possibly give you correct info to do the job right.
An engineer can calculate the loads & review the existing conditions & tell you what needs to be done. It sounds like your house may have cobbled together at some point & could need remedial work beyond what you see. One reason he charges what may seem a lot is the liability involved on his part when he tells you what to do. For that price you may not get drawings, but you should get sound advice & sizes for members.
Then you can turn it over to a contractor if the work is over your head. Or the engineer may give a bit of advice on how to proceed.

If you could post a picture it would help. Was the section that's cracking under an addition? Are all your support posts wood? Are the loads on this section different then the loads on the section with adequate support? What do the wood posts sit on?
Ron

Back in 1976 we bought a 9-room Dutch Colonial that was custom built in 1930. Like many houses of that vintage, it had sagging floors on the first level, and the 2 main beams in the cellar had bowed out of shape some. The broker who made the deal for us advised me to put telescoping supports under the beams at exactly their lowest point, and to lift the poles once a week by about a quarter of a turn, and continue doing that for a few weeks. Don't tighten the poles too fast, he warned me, or it could cause plaster all over the house to crack. I did as he suggested, placing thick steel plates above and below the poles so as to distribute the pressure. It seemed to work. We sold the house 10 years later, and never had any structural problems.

What does the beam that doesn't sag look like? And what does the part of the house that sags look like compared to the rest of the house?

If the part with the sagging beam looks like the rest of the house I would match up to the original beam.

$320 is money well spent to have a PE tell you what needs to be done. And yes, most of what you're paying for there is their insurance.. and it would cost more to get plans drawn up and stamped. You probably don't need stamped plans for this, unless your locality is VERY strict about permit requirements for this sort of thing.

I'll try to get some pictures posted up tonight. It's a working basement, so I'm trying to avoid using telescoping posts since that'll be right in the middle of the way when I'm trying to do laundry. At least I feel better about having an engineer come in and look at it.

As for the good section of the beam, it looks like three 2x8s that run nearly the entire length of the house. It's just as it gets to the last 8 feet at the back of the house that the post is smaller (something like two 2x4s stacked on top of one another). This doesn't support an addition, but there is an addition just beyond the end of the sagging section. But that structure looks to be totally separate from the main structure.

Either way, I'll try to post some pictures later on when I get a chance.