Hi,
fairly new into q8 but had been a stereo tracker for long time... if you already get the splice you're on the best position: remove the splice and wind up on a open reel the full tape, starting from the outside. Doing that way you will not stretch the tape. When the tape is on the reel, re-wind it in the original hub, of course starting from the centre. Rejoin both tape ends with the sensor foil and you're ok.
May i suggest one thing? Never play a newly bought 8 track without opening it first. I know sometimes it's so exciting to hear something you've sweared for years, if not decades, but two minutes more make no difference and can assure a proper life of a precious q8 cart.