Strong and weak functions not resolved correctly inside same library

Context: Compiling for an STM32 microcontroller using GCC (arm-none-eabi...)

I have a library that wraps the STM32 specific code (HAL.a), that code includes a startup file that declares the interrupt handlers as weak functions. I also have strong function implementations of the same signature in the SAME library. This library is linked to the application code. Unfortunately only the weak functions are ever linked, I cannot make it link the strong functions!

To show structure:

Application
  main.o
  (links) HAL.a
HAL.a
  stm32_interupts.c.obj
    void SysTick_Handler(void)
  startup_stm32.s.obj
    .weak      SysTick_Handler

The map file confirms that the weak implementation is always chosen. I have tried altering the order of the object files in HAL.a but it did not help (confirmed with arm-none-eabi-ar -tv HAL.a).

This is part of a much larger project built into many libraries using CMake so I cant mess with the structure unnecessarily and have limited control over linker command line.

Any ideas on how to resolve this?

I have seen a heap of posts on this subject but they all deal with having weak and strong implementations split between different libraries, and most offer no solution suitable for embedded (e.g. --whole-archive). They generally say to control the order of linking libraries on the command line but I assume I am achieving the same by controlling the order of the object files inside my library?

Thanks in advance...