For $75.00, I go for the fork if it's as nice as what you have now or nearly so. You won't (shouldn't) need a new headset because there's only one crown seat diameter standard for 1-1/8" headsets (that's a nice change). If you want to upgrade the headset while you're at it, now's a good time, but you cannot change to an integrated type bcause that requires a frame built for it.

If you go for the fork, buy a ton of spacers, and ride with the steerer overly long with spacers above the stem until your 100% certain you have the stem height where you want it, then you can trim the steerer accordingly and use the spacers for napkin rings.

The other option is to go for a steerer extender. Delta in the USA makes some (I might even have a NOS one in stock) and this is a good low cost option, especially if you have a decent quality fork.

My favorite option is to use a high angle stem. This is limited as to how much height you can gain, but may be the right choice alone or combined with a longer fork.

BTW- as you decide, measure carefully, and keep in mind that the general consensus for maximum amount of space below the stem is 1-2" (I like to keep it to 1" or so, unless the stem extension is short (LT100mm), then 1.5" is OK.