I have both sides as a runner and dog owner, never really had a problem with dogs while out running though and it doesnt bother me if they run up to me. If they were aggressive or bit me then I would restrain the dog and probably the owner too.
I own a lunatic of a parsons jack russell she is long legged and runs like a whippet, sometimes when she runs up to people in the park she can be a bit scary as she comes up really fast. We generally control here when small kids are about as she could jump up and scratch them or something. It's just about common sense and not letting your dog pester people.
Does she run up to people? yeah sometimes, but she is being friendly and she also comes back when called.
I did once have an incident where a women was walking her little terrier thing on the pavement and I was coming up to her from behind. I managed to swerve the dog but it ran right out in front of me with her lead taking up the whole pavement.
The owner yanked the dog back to her as I came past and it yelped. She then accused me of kicking her dog as I ran by, I didn't touch the dog and had to almost jump over it at one point.
Anyway don't be afraid of the dog be afraid of the owner, any dog no matter how big or small should be controlled around the public. Sometimes you can't always control your dog in terms of it running up to people but recognise when they arent happy about it and call it back.
The only thing thats going to help with endurance mate is running more mileage.
I was doing the same training for para reserves 1.5 mile in 9min 12sec and I found that doing 5K runs with a warm up finishing with doing the 1.5 miles as quick as possible was the best way to get my time down.
The endurance, tabbing with weight stuff can only really come with mileage. I used to pack up a bergen and go over the park with the dog, do some distance walking/running.
To be fair its probably the weights that are holding you back, you can't have both physically. Paras are trained to be fit, lean and strong not really bulky, the bulk will just slow you down. You don't sound too bulky but the leaner the better I would say.