Ha, so I need to get a volt meter in 10 μA range? You remind me that ages ago, when I was educated in college to become an engineer. I was told that any engineer worth his salt must always remember 6 words by heart: (1) Reliability, (2) Tolerance, (3) Accuracy, (4) Trade off, (5) Benefit, (6) Cost. Ah, I am missing my locking down lunch. Nice chatting with you. See you later.
I remember very vividly, that not too many years after my graduation, I learned many more things that I found very useful in my work, including the following:
(1) Appropriate Technology,
(3) Quality Control and Assurance,
(4) Risk Analysis and Control (MTBF, Black Swan Theory (sort of).
And the very important thing is the following:
(5) Info/Enggr System Analysis and Design(ISAD)
My journey in EE ended abruptly when most of the plants (including FairChild, Motorola, National Semi, Ampex, ...) closed and or moved North. So I switched to software engineering, then to IT, ... from transistor to IC, to MSI, LSI, to uP, to MCU, to SBC, to ...
Long story short, I am all the way back to transistor, to 2N2222, ...
And let me explain my 2N2222 temp sensor development with the following two things:
(1) User Requirement and Constraint,
(3) Selection of Development Methodology (WaterFall, Protopyping, ... Agile, ...)
What I am now messing around withe the OP's 2N2222 question is based on the Agile Methodology, which I see it as so called "Rapid Prototyping", or "Meddling Through",..
I also see the OP's question as a case study of PBL (Problem Based Learning) where I don't expect a clean solution. I think it would be nice, if me and the OP failed in all our suggested approaches, because we can "Learn by Mistake", the more mistakes we make now, the more lessons we learn, ...
I am just doing a selfie walkthrough of my electronics journey along a long and winding road, ...
Just brainstorming/thinking aloud, sorry for all the typo mistakes.
I used to tell the newbies that my project development does based on the expert's ideas, and the following is the text book I have been reading:
System Engineering Analysis, Design, and Development: Concepts, Principles, and Practices - Wiley 2nd Ed Charles S Wasson
https://www.amazon.com/System-Engineering-Analysis-Design-Development/dp/1118442261
For students such as the OP, I usually recommend the free 1st Ed eBook, because the basic concepts and recommendations by Prof Wasson are still up to date and very good.