IMHO, you are at ground zero, with those conditions. You know you have compacted soil and you know you have to add lime. You have to do some vertical tillage (sub-soiling, which has controversy of it's own) and you have to work the lime (conventional tillage) in to the top 4" - 6" of soil, where most of the roots are or will be. Lime doesn't melt and would take forever to get down in to the soil, by top dressing. It wouldn't hurt to get your P & K down in there as well.
Once you've got your compaction taken care of and your soil ph up, where it needs to be, you can do whatever no-till process you like. Just keep an eye on your ph and add lime on top of your soil, regularly, per soil test. Stay ahead of it. Under those conditions, any conventional tillage, the first year, won't set you back too far.
Choose your plants wisely, to help you. Choose a buffet that would include a cereal grain, daikon radishes, white clover, red clover, chicory and whatever else you like. Roots will help you break up the soil, as well as mine nutrients from below and add organic matter to the surface. White clover probably has the shallowest of those roots, maybe 6" deep, while red clover might be a couple of feet and chicory deeper yet. That kind of variety, will also help you, if you ever get a summertime drought.