Where am I going wrong?

You can't judge your progress based on single weeks: short term changes in weight reflect changes in water weight and food waste in your system. First week was extremely low calorie, with certainly a lot of water weight loss and also less food waste in your digestive tract. Increasing to 1200 then increases water weight and food waste again. And strength training is notorious for causing water retention in the muscles for muscle repair (3 lbs is well within normal water retention for strength training)

Stick to a calorie goal (hint: 800 isn't a good choice ) for at least 4 weeks and preferably 8 and see what happens. Also: take progress pictures and take measurements - the scale doesn't tell the full story.

You're used to restriction but you already have some idea that it's not the right way. You just need to stick with a more sensible strategy for a while

As @Lietchi said - consistently is the key (not going hard, losing energy, and giving up). Slow and steady wins!

Our stats are similar - I’m just a little older than you (52), and I was a little heavier (164.6lb) when I restarted back in November, and not as tall (5’5”), initially aiming for 147lb but recently adjusted to 144lb.

I put my stats into the MFP setup to lose 1lb per week (I was actually aiming for 0.8lb so I adjusted my calorie intake accordingly once I got started - perhaps one of the regulars can post how to calculate that?). I was eating about 1,350 calories a day throughout that period excluding exercise calories (of which I generally ate about 80% back unless I was particularly hungry). I ate a little bit more on a few special occasions/holidays, logging it all.

After the first 100 days I did some calculations to see how much error I was making in weighing my food or eating back from exercise, which I have put into the spoiler below.

It took only 189 days to get to my target weight ‘range’, and I’m currently in maintenance at the lowest weight I have ever been as an adult (average 143.9lb in July). It works. Trust the maths.

An interesting fact I read here on MFP: Your body can, at MOST, pull 31.4 calories per day from any given pound of fat per day to use for energy. Once you've multiplied that by the number of pounds of fat you have available, any excess energy used would have to come from muscle. Eating too little is not healthy for MANY reasons, but this one really shows how futile it is to survive on so little food. I’ll repeat what @Lietchi said - please rethink your strategy.

Wait 4-6 weeks at a consistent weekly calorie amount before judging how that amount is affecting your weight and body composition. As far as muscle you won’t be gaining much, if any while in a consistent calorie deficit so the key is to not lose what you have right now.