From the last few post form the OP it seem that booth the GM and the OP are equally to blame. The first issue was that the OP wanted to play a wizard, but the GM would not let him because there was already a wizard in the group. It also seems like the OP has a specific concept of what he wants to play, and is doing everything he can to make it work. The problem is that for what he wants to do a sorcerer really is not the right class. The OP seems to be aware of this, but is trying to make it work as best he can. He is looking for any way to salvage his concept, including misinterpreting the rules for spell research. His mistake was that he kept going with a concept that is not going to work with what he is allowed. The smart thing for him to have done would be to come up with a different character and save this concept for another campaign.
The GM also seems to be overly restrictive. Having two wizards in the party is not really any different than having a wizard and sorcerer. It is quite easy to create two distinctly different characters even when both of them are wizards. Just choosing different schools and opposition schools are going to make each character unique. Have each of the wizards have the others specialty school as one of their opposition schools and they are actually going to be more different than a wizard and a sorcerer.
The fact that the OP wants to go into Eldritch Knight also makes a big difference. In all honesty Eldritch Knight is a lot less powerful than a straight wizard. Losing two caster levels puts you a full level behind in spell access. Your stats are also going to be a lot different. Having to spread out your stats is going to put you further behind the straight wizard as far a power goes. Your combat ability will be better than the wizard but still well below a full martial class. It does give you a lot of versatility which the OP seems to value, but it is less powerful than the straight wizard.
If you're concerned "2 wizards" is a bad party so you're cajoling someone to play something else, that something else should not be a different 9th level arcane caster.
Though maybe a Wizard and a Witch would do fine, but a Wizard and a Shaman (not arcane) would probably do better.
It's just me or is this whole thing asking for some Tableflip McRagequit insight?You know, looking at this thread again, I believe this is what happened:
Sorcerer Player: I want to use spell research, so I can know a metric ton of spells I can cast freely. Wizards and their spell prep can suck it, I'm a font of eldritch power.
GM: Doesn't work that way.
Sorcerer Player: You are wrong, I'll use the powers of the internet to prove it!
Online GM's: Doesn't work that way. But you could do this or this.
Sorcerer Player: But I want this to work! Exactly the way I interpret it.
Online GM's: No, it doesn't, but here's some more ideas how to solve this.
Sorcerer Player: Screw you guys, I'm going home. This game sucks.
Hey! Yeah!