Before I start you will have to pardon my ignorance on some of the key points in your situation and be aware that the only information I have on this is what you tell me. Also be aware that if I suggest anything you suspect could go against doctor's orders or present any risk don't do it or get guidance before you try it if you do.
Chemo fried your thyroid making you hypothyroid, I know how being hypothyroid affects you but not if this is reversable after chemo. In my ignorance I will be giving guidance that should kick your metabolism back in the right direction if not fully into gear as if that is possible. If it isn't some of what I say should still help.
Start with diet. Low carb goes against everything the human animal has spent 3.5 million years evolving toward, please stop it. The logic for cutting carbs is based on two truths, excess carbs can be converted to fat and excess sugar is bad for you. Excess protein will be converted to fat or ditched in urine, fat doesn't need to be converted and neither can be burned as energy without being converted to something else first. All sugars are carbs but not all carbs are sugars, when I said we have evolved for high carb diet this is high complex carbs aka starch, found in wheat products, rice, potatotoes and most vegetables. This make carbs the good guys as you can burn these without them going to fat and there's more benefit still. The body is not stupid and knows we are designed for high complex carb diet, as such it assesses energy intake and therefore available energy by the amount of carbs you are taking in, pretty smart really. If the amount drops so does your metabolism to ensure you don't spend energy you don't have, keeping the level sensible prevents this drop.
If you want to lose fat cut down not out unless you are eating a ton of sugar or lard every day. Keep a good overall balance and eat a bit less of all of it. Drastic changes rarely work unless your diet is a disaster zone.
Activity for fat loss. Your mixed apporach is a good one, cardio and weight/ resistance will give a nice balance and help you accomplish what you want. You will notice I say fat loss not weight loss. Muscle is heavy, because it's largely made of water, and fat is compartively light so you can gain muscle and weight while losing fat. The only way to know this for sure is MRI scan, closest most get is bodyfat scales but often the best guage is the mirror which is hard to use well.
5 times a week could mean you are overtraining, but without knowing your program I won't know as variance of sessions can make this fine.
Heavy vs light is genetically biased. The main reason weights help fat loss so well is by building muscle that burns energy even at rest. If you are genetically set for lighter work then doing this will activate more fibres and make them develop faster, if you are more built for power you need to go heavy to work with your body, there really is no one size fits all. If you are designed to be large built and don't want to activate the bulkier building white twitch fibres then you will have to accept your progress will be slower. In the same way I decided years ago to build up and go for power, totally against my genetics, I have done it but it took me far longer than those more gifted. Basic lesson, you can do what you want only time changes.
Balance is very key and easy to get wrong especially at the start. There are good programs here, one of the stickies on the weight loss area by goldfish is brilliant. He is very good at generic guidance and comes with a lot of real world knowledge.
Activity will increase your metabolism too so can counter hypothyroid as long as the damage isn't permanent. The true irony, burning more energy makes you more energetic.
Mental attitude is very key and hard as hell to maintain when things appear to be going against you. Metabolism drop also causes chemical deppression, not helpful in the least. What this means for you is a real tough ride and those saying otherwise can help your workout program if you give them a good solid slap, of course make sure you tell them it's not personal just part of your workout routine. You need to ignore the negative and push on with dropping food intake gradually and increasing activity, knowing that even when you start doing well your mind will likely say it's not enough and the physical depression you are experiencing will make you feel like quitting daily.
This isn't sugar coated, I don't do that. The good news is success will come if you perservere and if the thyoid damage is reversible you will fix it and over time will feel a lot better. As I do with anyone willing to work at it I hope you go for it and do really well, not good luck just well earned.