The Glasgow centre spent three weeks in Philadelphia working with knee conditioning expert Bill Knowles as he bids to recover from cruciate ligament damage.
Alex's World Cup hopes have been under serious threat since he suffered a freak injury ahead of Scotland's trip to Twickenham to face England in March.
The 25-year-old is still training on his own but is now doing so in the immediate vicinity of the Scotland training squad and hopes to get the all-clear from a specialist to join them within the next fortnight.
Alex said: "This is my first chance to play in the World Cup. If I can keep pushing and progressing well, it could hopefully be a dream come true.
"That's the hope just now. It's going well, I feel quite positive now and hopefully I can make it.
"I have still got to see the specialist and still got a lot of fitness work and conditioning to get through before I'm fit to take part in full training. I'm happy where I am at the moment but I know there are still a lot of boxes to tick before I can get back out playing."
Alex went from gym work and band resistance work to running and changes of direction in the United States.
"It was good to get the boots back on last week and do a lot of running and drills out on the field," he said.
"It's been tough being in the gym just doing rehab so to get the boots back on and be able to run about again was a great psychological boost.
"It's good to be back in with all the boys. Obviously I can't do the same sessions they are all doing but I'm just off to the side doing the band stuff myself and working with the physios trying to keep pressing along.
"The plan is to pick up a few things from training and meet some of the new boys. It's good to be part of it, it keeps you going along."
Alex experienced a major high in a Scotland jersey last year when his second-half pair of tries earned a 21-20 Six Nations victory over Italy.
But his lowest moment came 13 months later when his knee gave way without warning while running in a light training session.
"The first two or three weeks I was pretty numb with how it all happened, how it could go so soon just jogging about," he said. "I couldn't believe how it happened.
"It has been tough going. There were a lot of days at the start where it's sore and you can't do a lot and it's boring a lot of the time. But I have been quite positive. Any chance I get to progress has been good and gives you a little boost.
"It was disappointing watching the end of the Six Nations, but to go back to Glasgow and see the buzz about the squad going into the (PRO12) final and winning it was unbelievable. That gave me a boost to keep me pushing on."