There are ways you help with this but to be honest it'll be too expensive for the little gain you will get.
The cheapest way to help with performance as with all cars is to reduce weight. Don't load your car with any unecessary weight, things some people have done include: replacing spare wheel and jack with tyre weld, remove rear seats, change battery (already quite lightweight - but some have gone for far lighter supercapacitor ones), lightweight wheels etc...
Looked at lithium battery for my motorbike, certainly lighter but at over 4 times the price of the standard Yuasa lead acid to save maybe 300gram a total waste of money (and Boeing Dreamliner airliner fires were caused by Lithium batteries ). Would never willingly replace a perfectly good spare wheel with tyre weld either. If you are into tuning you need to get VTEC lump and get it chipped - defo cheapest way as the engine is 12/16V as standard (for economy one inlet valve stays closed till about 3.5K then starts to work - making more power but using more fuel - chipping can bring VTEC point to lower revs and increase injector times etc )
I wasn't thinking of lithium batteries - which I suppose if you're desperate you could consider. You may not be aware, but "super capacitors" are really gaining momentum and some have actually built ones that can start a car consistently well. These weigh a fraction of the OEM battery.
But as for lithium batteries, there are different types. Generally Lithium Cobalt Oxide, Lithium Nickel Manganese Cobalt Oxide and Lithium Nickel Cobalt Aluminium Oxide? LiCoO2 is considered less safe at high discharge and gets hot which I suspect could have been used in the incidents that you mention. But in terms of energy density, they are very good.
Tyre weld is fast becoming popular alongside run flat tyres with OEM manufacturers. My car (BMW 1-series) came like that and I think BMW are heading in that direction now to save weight and the need for road side repairs.
As for changing the engine, I agree having a vtec engine is by far the best way to get extra power and is more flexible in turns of tuning. Although staying with an NA vtec engine will only get you so far - as I found with modifying my EP3-R over 7 years. I think the OP just wants a little more power, and especially torque at low revs - not a track animal. So I guess changing the engine is probably not an option... ?