In short, no configuration using PPTP should be considered secure.
Firstly, setting a low idle timeout is not a mitigation against a MITM attack. The idle timeout setting just determines how long the server will allow an idle session to remain connected (and setting it to
0 will actually probably disable the timeout entirely in most implementations). It has no direct relationship to latency. What's more, an ARP poisoning attack (to establish MITM) may not look that different from any normal hop along the route anyway, so latency is a difficult side-channel for detecting this kind of man-in-the-middle outside of a fast, predictable local network. The kind of MITM attack required to break PPTP is much simpler than, say SSL, where the stream needs to be de- and then re-encrypted. The attacker simply needs to capture and forward your packets to break your connection.
The trouble for you with PPTP is that even in its "most secure" arrangement it is utterly broken (see Are there any known vulnerabilities in PPTP VPNs when configured properly?). A successful MITM can not only impersonate you to the VPN, but it can decrypt any captured sessions, which will include the passwords or any other credentials that you need to send to the destination.
So the answer to your question is a resounding no, PPTP cannot be considered secure in any configuration.
Since your options seem limited, though, you may decide that PPTP can be secure enough for your use case. Just be aware that if your connection passes through a malicious connection, there are tools available that can automatically sniff and crack any PPTP sessions. It might not be likely, but if you're unlucky, PPTP is so insecure that you needn't even be specifically targetted, you could simply be a target of opportunity. It really is that insecure.
My VPN client only seems to supported PPTP and LT2P with IPSEC policy.
It seems to me you should really start here. You need a better client.