Thought I'd post a TR on this trip I did back in September shortly after the restrictions on travel into Myanmar via Myawaddy were lifted.
I do recommend this trip as an alternative to flying into Myanmar - very easy to self-organise or through an agency, affordable and scenic!
Crossed over early, around 7am, from Mae Sot to Myawaddy. Immigration was smooth and painless. The money changes were closed by a 24 hour KBZ ATM is on the left hand side down the road after you clear the Myawaddy immigration so it's easy to access local currency.
If you haven't already organised transport (and my understanding is it's cheaper going from Myawaddy to Yangon than the other way around), you'll get plenty of offers for transport, with different vehicle types, quality and prices. A negotiated 20,000 kyat price got me a nice car on a trip to Hpa-An, with a driver who spoke decent English, air-conditioning and two Burmese passengers in the back who slept most of the way! Just check when the car is actually due to depart, otherwise you may be waiting around for a while as they try and get more passengers for the journey. I didn't enquire as to how much a total journey to Yangon would cost, but remember the driver will have to overnight in either of Hpa-An or Yangon and return, which must be factored into pricing, plus fuel costs.
Traffic on the Myawaddy-Kawkareik road (which winds through the mountains and is a beautiful but rough and bumpy ride) goes in different directions on alternate days, which you need to factor in when planning your trip! I do recommend a nice comfortable car for this part of the trip; a friend took a bus and it apparently was not the most pleasant journey he's ever had! But you are very high up with spectacular views and pass villages and monasteries on the way, and is an experience to be done at least once.
There also seemed to be restrictions in place on where you can stop - I wasn't allowed out of the car except at checkpoints (of which there were a few on the way) and a specific teashop in Kawkareik.
In all it took around 5-6 hours from Myawaddy to Hpa-An, stopping at Kawkareik for lunch. My original plan was to spend a few days in Hpa-An, but the weather wasn't ideal so I ended up taking an overnight bus to Yangon, which was typically cold, long and tiring - it's 4 hours direct by car and 7+ by bus. In Hpa-An I was offered 10,000 kyat for a seat in a car with 4 others (inc. driver) back up to Myawaddy. Shows the variation in prices but it'd be a cramped ride!
When you're in Hpa-An, check out the Kaw Ka Thaung caves (accessible via a road that takes you past hundreds of monk statues in a very long line), and most importantly the stunningly beautiful lake area behind it; it's breathtakingly beautiful. Mount Zwekabin was out, as it was too cloudy. But it's on my list for next time, hopefully before the cable car is built!