WireGuard: three peers connected linearly, UDP over TCP for one connection only

I have three peers on a WireGuard network:

• Peer J is behind a standard corporate firewall blocking all outgoing UDP,
• Peer S is a server with static IP, and
• Peer P is my smartphone.

   No UDP out;
  +-----------+  (Static IP)
  | Peer J ---|--- Peer S ------ Peer P
  +-----------+         [Regular wg]
So, UDP over TCP

I want to connect peer P to peer J (P ssh into J) via WireGuard, where J and S are connected by UDP over TCP (using wangyu-/udp2raw), while S and P have a vanilla standard WireGuard UDP connection.

Here's my attempt thus far:

Peer J

[Interface]
# PublicKey = E8K...
PrivateKey = ...
Address = 10.0.0.6/24
MTU = 1342
PreUp = /usr/bin/udp2raw -c -l 127.0.0.1:50001 -r <S's internet IP>:443 -k "secret" -a >/var/log/udp2raw.log 2>&1 &
PostDown = killall udp2raw || true

# Peer S
[Peer]
PublicKey = Yf3...
AllowedIPs = 10.0.0.0/32
PersistentKeepalive = 120
Endpoint = 127.0.0.1:50001

Peer S

[Interface]
# PublicKey = Yf3...
PrivateKey = ...
Address = 10.0.0.0/24
MTU = 1342
ListenPort = 80
PreUp = /usr/bin/udp2raw -s -r 127.0.0.1:80 -l <S's LAN IP>:443 -k "secret" -a >/var/log/udp2raw.log 2>&1 &
PreDown = killall udp2raw || true

# Peer J
[Peer]
PublicKey = E8K...
AllowedIPs = 10.0.0.6/32
PersistentKeepalive = 120

# Peer P
[Peer]
PublicKey = wlx...
AllowedIPs = 10.0.0.19/32

Peer P

[Interface]
PublicKey = wlx...
Address = 10.0.0.19/32
MTU = 1342

# Peer S
[Peer]
PublicKey = Yf3...
AllowedIPs = 10.0.0.0/24
Endpoint = <S's internet IP>:80

Problem: Peer P cannot ping peer J. But peer J can ping peer S and vice versa; and peer S can ping peer P and vice versa. The traceroute of P to J is:

raceroute to 10.0.0.6 (10.0.0.6), 30 hops max, 60 byte packets
  1  ip-10-0-0-0.region.compute.internal (10.0.0.0)  54.950 ms  54.063 ms  53.245 ms
  2  * * *
  3  * * *

So there is something wrong with the routing at S, but I can't figure out what exactly the problem is.