Now the question is, can I mine enough in the first couple of weeks to *fingers crossed* future proof myself against a sudden rise in difficulty, which will lead to a rise in price
Why do you think a rise in difficulty will lead to a rise in price? I think if anything it's the other way around, and even that is tenuous.
Difficulty is calibrated against block rate, so on average we get a steady block rate and a steady 1200 LTC per hour in mining rewards regardless of other factors. If price goes up then there's an increased short-term incentive to mine and more miners will participate, leading to an accelerated block rate, then an increased difficulty level, which in the longer term leads to lower revenue per miner, probably balancing out at roughly the same real-world level as before the price increase.
But I'm not sure the converse is true - a rise in difficulty indicates prior increased mining activity, and acts directly to balance it out, but I don't see why that would affect the trading value of the coins. If the difficulty rise wasn't due to a price rise as above, then miners would find it less profitable in real-world terms and may get out of the game, leading to a difficulty reduction. If anything, the price of the coins would drop though, if the quitting miners sold their coins.
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