The `Broadcast`/`ResendWalletTransactions` interface is strange:

- it's the node saying to the wallet "Try to submit your unconfirmed transactions to the mempool again"
- it's called in one place by the node, in `SendMessages()` here: https://github.com/bitcoin/bitcoin/blob/c033c4b5cef89a654e4d9d5c5f9bd823871b068b/src/net_processing.cpp#L3515. `SendMessages()` is called on the message handling thread on a loop.
- the actual scheduling of when the wallet sends messages is handled in the `ResendWalletTransactions()` function itself, using the `nNextResend` and `nLastResend` wallet globals (which could as easily be static variables in `ResendWalletTransactions()`).

Therefore the only use of `Broadcast()` is to periodically prod the wallet. The wallet itself decides whether it's time to resend transactions. This could be done by scheduling regular calls to `ResendWalletTransactions()`, in the same way that we schedule regular wallet flushes here: https://github.com/bitcoin/bitcoin/blob/c033c4b5cef89a654e4d9d5c5f9bd823871b068b/src/wallet/init.cpp#L215.

A couple of minor implementation details:

- the call to `Broadcast()` in `SendMessages()` is protected by an if statement `if (!fReindex && !fImporting && !IsInitialBlockDownload()) {`. Those tests could be moved into `ResendWalletTransactions()` (through the `Chain` interface).
- The `Broadcast` notification passes in the `nTimeBestReceived` time of the best block. That could be fetched by `ResendWalletTransactions()` through the `Chain` interface.
continue;
                }
                int64_t nSmartTime;
                nSmartTime = pwtx->nTimeSmart;
                if (!nSmartTime) {
                    nSmartTime = pwtx->nTimeReceived;
                }
                if (nSmartTime <= latestTolerated) {
                    latestEntry = nSmartTime;
                    if (nSmartTime > latestNow) {
                        latestNow = nSmartTime;
                    }
                    break;
                }
            }
            nTimeSmart = std::max(latestEntry, std::min(blocktime, latestNow));
        } else {
            WalletLogPrintf("%s: found %s in block %s not in index\n", __func__, wtx.GetHash().ToString(), wtx.hashBlock.ToString());
        }
    }
    return nTimeSmart;
}
bool CWallet::AddDestData(const CTxDestination &dest, const std::string &key, const std::string &value)
{
    if (boost::get<CNoDestination>(&dest))
        return false;
    mapAddressBook[dest].destdata.insert(std::make_pair(key, value));
    return WalletBatch(*database).WriteDestData(EncodeDestination(dest), key, value);
}
bool CWallet::EraseDestData(const CTxDestination &dest, const std::string &key)