If going with your solution seems best as to what your Line Manager is proposing, should you still push forward and take your own proposed action?Why?

This is a typical situation where one ought have to put perceptions and respect aside and analyze thoroughly. It is actually a good thing that your line manager is proposing a solution as well as you also have a different solution. Instead of making it personal , one must examine all the options analytically listing down all pros and cons. Once it is there, it is always a good idea to discuss all options on the table with your line manager. Also, you should be accommodating if his approach is better as nothing shall be carved in stone. Every decision must have analytical backing.