Alright let's be 100% honest here. I'm glad that you have goals what will both make you healthier and stronger. But we must evaluate if they are realistic.
Adding 100lbs to your deadlift in roughly 3 months, or about 20% in your case would be a VERY lofty goal if you were devoting all your energy to getting stronger (which means no extra work and plenty of food to grow). Normally during a 12 weeks cycle the gains to be expect for a non-beginner on a lift like the deadlift is between 7.5 and 12.5% (I've seen up to 15%) and that is while eating to gain strength and size and not doing any activity that would hurt recovery. Heck, the stronger/more advanced you are the harder it is to add pounds of the bar. I know several world class powerlifters/strongmen who are happy to add 5-10lbs to their lifts in 12 weeks.
So for someone who deadlifts 450 we are talking about adding 30 to 50lbs (maybe 60 on a good day). And again, that is under optimal strength gaining circumstances.
The "good news" is that the deadlift is NOT really affected mechanically by a loss of weight.
Now adding 50lbs on your overhead press in 3 months is, from my experience, even more unlikely. The strict press is the movement that increases at the slowest rate AND pressing exercises are highly affected by loss of weight.
So in 3 months a gain of 15-20lbs is a lot more realistic (we are talking strict press, no cheating), maybe 30lbs. But again these would be under optimal conditions.
Now let's look at your situation objectively.
You will be hiking 5-10 miles a day (whicfh is a lot harder than just walking)
You will be hiking in very hot an humid conditions (which fatigues the system even more and dehydrate you, which affects strength)
You will be hiking in very hot and humid conditions while being over 300lbs... when you are heavier it is much harder because you have to carry that weight
You will be doing an intership which likely means working 30-50 hours a week
You want to lose a significant amount of weight (40-50lbs)
You likely wont have access to a gym of the same quality as you did, and there wont be as many strong guys aroud. This plays a huge role in progression.
These 6 things will make it A LOT thougher to gain strength.
The one thing that plays in your favor is that you are getting back to the gym so your body will respond well.
Honeslty if youi maintained your strength while dropping a good amount of weight under these conditions I would consider it a success,
Adding 30lbs on your deadlift and 15lbs on your press would be very good.
I'm NOT saying this to be a downer. But to keep you from making bad decisions.
When you set unrealistic gials for yourself and you see tha you are not on pace to reach them you tend to make somne emotionally charged decisions that can hurt your long term progress even more.
It can also kill your motivation which hurt your training performance.
When you set goals it should NOT be like this:
"I'd like to add 100lbs to my deadlift and 50lbs on my overhead press. And losing 30lbs of fat would be great, so these are my goals".
Goal planning is a very serious thing. You don't just throw numbers around because they shound good. There is no such thing as "shooting for the stars you will at least reach the moon"... missing the starts because they are too high can have a lot of neative impact on your self-estemm and motivation to train.
When you set a goal you must analyze your previous experience to know what is possible.
- How much strength did you add on your deadlift and overhead press these past 3 mionths? If it is significantly less than 100 and 50lbs what makes you believe that you can reach those numbers now that 1) you are more experience thuis progress is slower 2) you will be in very bad conditions to add strength?
If during the last 3 months you added 50lbs to your dead and 15lbs to your press, while doing very littlke extra activity and maintianiung or gaining weight, how much strength dio you objectively think is possible to add in 3 months while losing weight and doing plenty of extra activity?
- And if you did gain 100lbs on your deadlift and 50lbs on your press these past 3 months, did you do it while also losing fat and living on a super hot and humid environment? Because even if you did manage to add 100/50 to your lifts in 3 months, you have to understand that it is much harder to continue progressing this way especially when the conditions are not optimal.
So when you look at your history, look at what is your average strength gain over 3 months. And you should use slightly lower numbers as a goal. Why lower? Because goals need to be achievable. You will be training is MUCH WORSE conditions than the previous years of your training life. And you will be doing so while trying to lose weight. It is impossible to gain at the same pace as before. I much prefer to set more realistic goals and exceed them then come up short of overly optimisitic ones.
So realistically you might shoot for a 30lbs gain in deadlift, 15lbs gain in press and a good amount of fat loss (I don't know how much you want to loise). And that would be VERY GOOD under the circumstances.
And do not forget: if you are in this for the long run, who cares what you can lift in 3 months???