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So my biggest dilemma is should I buy a new clock or a helmet for myself.
Get a new clock, and give it to her along with the receipt for it, to replace the property she's destroyed. Works best if her birthday is coming up shortly so you can give it to her then.
(As you may be able to tell, I'm no parent. By choice.)
Not that I'm a morning person myself, but I've never had to rely on an alarm clock. I've probably been awake before 6:00am / 6:30am every day of my life without ever trying. Not that I get up at that time. But by the time I need to get up, I've already done enough tossing and turning to get up without any hassle.
Buy her a nice bicycle that'll substitute for the taxi service you provide when she misses the current mode of getting to whereever. The incentive to get out of the rack in the morning is the first hurdle.