If the multiple upgrades isn't possible then perhaps a completely progressive government system would work. Again in diagram form:
COMPLETELY PROGRESSIVE GOVERNMENT SYSTEM:
Type 4 => Type 3 => Type 2 => Type 1.
(Type 4 upgrades to type 3, which upgrades to type 2, which upgrades to type 1 - n.b. adjust the time to build and cost to build accordingly so that both build time and cost to get to Type 1, Type 2 or Type 3 is still the same as in the current system)
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