Re: techniques to use against a front chest push?
In terms of training traditional forms and developing the ability to respond to "any" attack, the fact that traditional attacks are stylized implies to me that any single one is not going to make you proficient at improvising effectively against an attack with a very different form. Practicing the kind of stylized "shoving attack" seen in some of the posted video likely would reduce the chances of freezing if you did need to respond.
Another example -- ushiro ryote dori irimi nage is a bit different than shomen uchi irimi nage and training in one won't teach you everything you'd like to know about another.
As to shoving as an attack, I have to agree with Mary -- impossible for me to say in the abstract whether its an "attack" you need to respond to or not. I've been shoved up against a wall, hard; I can see how it could be the start of something serious.
As for tiger balm, if you just pulled an all-nighter but have to attend a class or meeting, a small dab on the forehead can keep your eyes open even when you are sleeping. It doesn't help so much if you're called upon to say something half-way coherent, though. And you still need to be careful where you place your fingers after applying.