I am a sports chiropractor and saw your post.
I understand what you mean by the pain being between the two typical spots. It is possible to get a partial tear in just the outer part of the patellar tendon under the knee cap which is most likely what is going on. Does the pain feel very superficial like right under the skin? or does it feel deep to the knee? Deep knee pain would make me nervous about meniscus or bone issue. Chances are slim that's the problem. It's probably the tendon.
No improvement after 6 weeks of conservative PT would get me thinking about a potential meniscus tear which can technically be felt between those two points if the pain is also in the joint line. If I saw him in my clinic today, I'd have him go get an MRI.
Is your PT doing a lot of physiotherapies in addition to the exercises to help promote healing like ice, heat, muscle stimulation, ultrasound and/or cold laser (low level light therapy)? I've personally had good success with cold laser on superficial injuries like teninitis. You may also consider having it kinesio taped (that colorful tape stuff you saw a lot in the Olympics). I use techniques like Graston/ASTYM and Active Release Technique on these types of injuries as well with good results. You may consider asking your PT about them.
If you don't do lots of therapies in PT, then you should be doing them like crazy at home. Switch ice and heat for 15-20 min at a time multiple times a day with an hour in between. If he can handle it, do ice massage directly on the skin until it's numb (usually 4-5 minutes). Don't over do it. Be careful how often you're fully flexing the knee (heel to butt) even with PT stretching - that stretch is putting the most tensile stretch on the damaged tendon. This isn't a stretching problem. Consider TENs unit for home stimulation. I agree that arnica is a good topical. If massaging the tendon feels good, I would do self massage quite often. Don't forget this tendon is an extension of the quad muscle on the front of your leg. I would massage and or foam roll the quad quite often to get the quad as relaxed and lengthened as possible to get pressure of this tendon.
Sorry for the long response. I hope this helps a little. Best of luck.