You might like to try coming at this from a slightly different angle by loading your object using preloading.
Set LD_PRELOAD to point to your new object
export LD_PRELOAD=/my/newfuncs/dir/newfuncs.o
and specify the existing library in the same way via your LD_LIBRARY_PATH.
This will then instruct the run time linker to search for needed symbols in your object before looking in objects located in your LD_LIBRARY_PATH.
BTW You can put calls in your object to then call the function that would've been called if you hadn't specified an LD_PRELOAD object or objects. This is why this is sometimes called interposing.
This is how many memory allocation analysis tools work. They interpose versions of malloc() and free() that records the calls to alloc() and free() before then calling the actual system alloc and free functions to perform the memory management.
There's plenty of tutorials on the interwebs on using LD_PRELOAD. One of the original and best is still "Building library interposers for fun and profit". Though written nine years ago and written for Solaris it is still an excellent resource.
HTH and good luck.