Hi, Jennifer,
Most homes do indeed operate at negative pressures due to a combination of stack effect, undersized air returns on HVAC systems and a lack of make-up air for high-volume exhaust blowers such as range hoods and dryers. I have never seen a home with a positive pressure HVAC system, but they do exist. I don't think you'll need to go to that trouble.
I suggest you carefully consider the addition of a supplemental lint trap in your dryer exhaust. It will add pressure drop which will affect both air flow and drying time. Most, if not all, are designed for applications where there is a booster fan installed in the exhaust duct. If you don't have a booster fan, I'd pass on that suggestion.
Altering the height of your dryer exhaust vent above grade won't do much except cost you a lot for a brick mason to patch up a small hole. If the exhaust location is causing a problem, you'd see lint in the attic (there's a continuous soffit vent located directly above it which is how ventilation air enters the attic.) I don't believe you observed lint in your attic so moving the vent isn't likely to affect anything.
That said, the dryer vent cap is in a location that makes periodic inspection and maintenance a pain. I suspect the damper at the exhaust vent is either stuck open or is being kept from closing due to an accumulation of lint. That would allow back flow through the vent when the dryer isn't operating and introduce lint into your home. I saw this in one home where the backflow of hot, humid air caused condensation--and lots of it-- inside the dryer in the summertime. I recommend you start by swapping out the cheap-o vent cap for one that seals better when closed. Here's my favorite:
https://dryerwallvent.com/?ga=103960&gclid=EAIaIQobChMIu_KYz4Hc9QIVdcqzCh1oLAQnEAMYASAAEgK7vvD_BwE
Q