The trio of clubs - taking on Bromley, Royston Town and Wealdstone - are all bidding to confirm their berths in the second round in first round replays.
A waterlogged pitch at Southern League North Leigh put paid to South Park's bid to reach the latter stages of Non-League's showpiece cup competition after Christmas.
The Ryman League's other surviving flag-bearers - AFC Sudbury, Harlow and Worthing - are already through after their wins at the weekend and preparing for big home ties on Saturday 14 January.
To stay in touch with Tuesday night's league and cup action, log on to the Ryman League's live scores service via the home page. Alternatively, follow the Ryman League on Twitter @OfficialRymanFL.
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