If independent contract work was complete Dec. of tax year, but paid following Jan, when would I see 1099-Misc? In which year should income be claimed & expense deducted?

If you use the cash method (like almost all self-employed people, you report as income amounts received in 2018 and deduct expenses paid in 2018.

In your case, if the work is completed in December 2018 but only paid in 2019, you will receive form 1099-MISC for this job only in tax year 2019 (in January 2020) and will report the income on your 2019 tax return.

If you have expenses for this job which you paid in 2018, you can claim these expenses on your 2018 tax return.