A lot of people really kick back on sortition. I think a good compromise is this: everyone votes like normal. We then take the top K candidates who got more than some fraction of the votes. (Say: greater than 1/9th of the total votes.) The winner is selected, at random, proportional to the number of votes they received. Such a system would really really on having a large number of candidates on the ballot; my preference would be (in party ballots): top 2 (or 3!) candidates from each party, and any person who can get more than T signatures. (Where T is some number like “20000” or “5% VAP”.)
That compromise has all the downsides of both systems without preserving the upsides - it creates a pool of candidates that will be biased towards narcissistic lunatics but no democratic checks so they can get in to office even if there is a consensus that their policies will be destructive.
It isn't a terrible idea; I've long liked that sort of plan as a fallback in very tight elections to randomly decide between the candidates. But it isn't really a compromise with the sortition folk because it doesn't have the properties they're looking for.