I have used your test image of the Indian head. I'll make the following observations which you are welcome comment on or to ignore as you wish.
1. The images you provided are indexed color or rgb.
2. I don't recall you mentioning if or how you may have dithered them.
3. The wiring you show is not standard. You don't need the jumper from pin 5 of the L1 to pin 1 of L1. You are tying that to ground. In the Minimum Connections documentation (attached) from Light Object, pin 5 is not connected at all.
4. You board appears to be exactly the same as one of mine. I am using L1 pins 1,3,4 (three going to the TTL input). The others just as you have them. If you are using TTH, then you want pins 1,2, 4 as you have them, but without the jumper between 5, and 1.
5. You comment that you are getting nothing but solid burns, means you will never get good results until you get your wiring correct. (Seems you have already rejected the idea of fixing that first, but if you can't control the output, how do you plan to get usable results?)
6. Don't recall you mentioning what material you were trying to engrave on.
7. I don't think you need additional test files. The one(s) you have are fine. If you can't engrave them, you won't be able to engrave anything else either.
(EDIT- I had the TTL vs TTH incorrectly annotated in Tim 4 above. Now corrected. )
Here is your Indian head file, cropped to the head only, 2" wide. It was engraved at 100mm/s, 30% (works out to 10.9 mA on my setup). Dithered by LaserCAD (or probably PHCad, in your case) at .04, with a scan gap of .04. It is done on Baltic Birch craft plywood.
The first thing I would (again, you are welcome to do as you wish) is to disconnect pin 5 on the Laser 1 output of the DSP. Then try your file again.
I also ran your full IndianHead test pattern file, scaled down to 2" wide. Ran it the same as the above settings, but dithered at .10 and a scan gap of .10. Considering how small the image it, it turned out pretty well too.