There are a number of Chinese generic activity trackers containing the Nordic nrf52832 MCU and a GPS module which are easily hacked and would meet all your needs. Search for "nrf52832 gps bracelet" or "nordic gps bracelet" on Aliexpress, Banggood, ebay etc. For example: https://www.aliexpress.com/item/KINCO-OLED-GPS-Activity-Trac...
Components: Nordic nrf52832/ARM Cortex M4 MCU, Kionix KX023 accelerometer, Ublox GPS module, 200mAh battery, 0.96" OLED screen.
This can be programmed using the Nordic SDK with Keil, ARM mbed, Sandeep's Arduino Core for nrf5X etc.
Might be easily hacked, but has anybody hacked them?
I contacted a few sellers on Aliexpress because I wanted to see how many I had to order to get them to give me the source code so I could make a value-added product from them but it was beyond what I was willing to invest.
I have hacked the MCU and accelerorometer. Haven't gotten around to the GPS yet, lots of projects and this isn't at the top of the list. Its just hardware, all the components are well known, you can just lookup datasheets and go from there. I can post microscope pics of the PCB if you like. What is the best way to post/link pics on HN?