Hi! A lot of my customers in the construction industry run into the same problem. The dollar amounts, any legal considerations, and other factors, should all be considered, and I'm sure will make a difference in how applicable these suggestions are to you.
I would look into, or test, the following:
1. Changing your receivables process may rely on key Sales Process improvements. I'm happy to talk it through with you, and help you find the right solution.
2. You said it, but the first/best option is to make your customer the bank. Have them pay in draws/milestones/stages (whatever lingo their comfortable with) to cover your costs, and ideally pay you, as you go.
3. Offer a discount for paying the job up front and in-full.
4. I understand the bank offered a very small line of credit, but I imagine you'd do a bit better with a credit card. Estimate the monthly debt servicing cost per job, and charge your customer accordingly. This gives you the option to offer a discount if paid in full and upfront, without affecting your actual price or profit. ONLY exercise this option if you are disciplined enough to use the credit extended to you as intended and responsibly.
5. If you have a way of securing the short term debt, or maybe even if you can’t secure it, see if anyone you know who has some cash would be willing to buy options on your jobs’ profits or keep a running secured line of credit with you. If you don’t have anything with which you can secure a line of credit, see if working with an investor with small amounts at first, will lead to a trust and understanding of your business, that could lead to bigger amounts.
Examples- You win a job paying $100K, but it will cost you $50K before you collect the payment in full 30-60 days after winning the job.
a) You own a work truck worth $130K - use it as collateral to borrow $50k from an investor at a reasonable rate, for 30-60 days at time, to cover your costs until you can collect the full amount rom your customers.
b) Sell an Option on X% of the profits. In this example, the investor buys the option for $50K, and you guarantee, let’s call it 3% of the profit, plus their initial investment. When you get paid the full $100k, they get $1,500 plus their $50K original investment back. If you make more, they get a little more. If you make less, they get a little less.
I'm happy to jump on a call to talk through more solutions that fit you best or to follow up.

I’m not a legal or tax professional or expert. Do your own research and consult with someone who is a professional before using any of the ideas above.

Instead of Invoice factoring, I think you should focus on the problem on why project expenses are weighing you down. What are the factors that lead you to it? Are there unnecessary project activities which are currently included in your small business that are consuming a lot of your expenses?

Expenses are inevitable when you are into business, but you can cut them by laying all the unnecessary activities in running your business.

You have mentioned that you travel around the country, then transportation expenses are one of the main reasons why expenses weighs you down. I propose that if this is so, I think you should plan of your itinerary very well by cutting your several visits. What I am saying is, instead of paying a visit of more than twice a month to attend your business in one location why not make a plan that could make you visit just only once. By doing this, you can now cut the transportation expenses that burdens you somehow.