Lethargic Man (anag.)

In my last blog post, I referred to the genitive in Biblical Hebrew always being identical to the nominative. So says ewt's copy of Weingreen's Practical Grammar for Classical Hebrew; however I have possibly found a counterexample.

The phrase בֵּית הַמִּקְדָשׁ is pronounced "béth hammiqdāsh" (to use Biblical pronunciation); however, מִקְּדָשׁ by itself, for example, in the Song at the Sea, has a geminated^* ק, which makes the שְׁוָא a שְׁוָא נַע; hence the word is "miqqədāsh". By contrast the former example, which is in the genitive, has no gemination on the ק and a silent שְׁוָא נַח.

* Gemination is doubling of a consonant, and its length: think of the length of the N sound in "unnamed" in English compared with in "un-aimed".

Why is this so? The change in the שְׁוָא is probably to do with the gemination; but why is the ק geminated in the nominative, and why is the gemination lost in the genitive? Or is it to do with the presence of the definite article rather than it being in any particular case? Does the presence of the gemination of the מ caused by the definite article "drive out" that of the ק? And why is this rule not given in Weingreen?

Any grammar geeks out there?