Let not get carry ahead of ourselves here for a second because you like Japan, all right? Building F-2, a derivative copy of F-16 with full license and ToT, is very different than doing it yourself, especially in the realm of 5th gen fighter. Russia has a long history of aircraft experience and still having trouble with 5th gen, as we speak here.
The ToT between US and Japan is more one-sided. US only used selective Japanese technology while 70% of US technology is being present to Japan. For example, Japan produced about 30% of Boeing 787 which has the same complexity as a 5th gen fighter imho.
P1 is a patrol aircraft. Powering that plane doesn't need "state-of-the-art" engine. Let remember that. You can't use core engine from IHI F7 to make 5th gen engine because it is a high-bypass engine to begin with. In fact, IHI F7 core comes from the low-bypass IHI XF5. Though, the IHI XF5 doesn't have high-thrust to power a real 5th gen fighter. The ATD-X model is said to be powered by XF5 but we know that this is a "wood model" or "toy model" if you want to call it. Expanding the size and power of XF5 will increase the complexity of the engine. That is the rule. Anyhow, depending on how much the US will help them, it is remain to be seen. Like I said at least 2-3 decades is needed for a mature 5th engine. Japan only start their 5th gen engine program now and want to jump into the penhouse of a high building? No way!
I bet if the US gives us full access to the F-35, we would make a better F-35 on time and on budget right now.