I'm not a native speaker, so there may be errors in my observation.
Strictly speaking, the examples you gave is not lengthening, but inserting. I think they are not predicable, but explicable.
There are generally two types of sounds that can be inserted, っ and ん. っ is used before unvoiced consonants such as k, t, p(h becomes p), s and sh. ん is used before voiced sounds such as b, d, g, n, m, z, w, j, etc. As for voiced stops like b, d, g, old words tend to use ん, while new words tend to use っ.
Most adverbs consist of three syllables. Many can be emphasized by inserting a syllable after the first one. What syllable to be inserted is not fully predicable. You must look up in a dictionary to know them.
You may be especially interested in ～ん～り/～っ～り words.
Apart from those ～ん～り/～っ～り words, some other words, especially intensifiers, have their emphasized forms, too.
やはり【LHL】 → やっぱり【LLHL】
あまり【LHH】 → あんまり【LHHH】
とても【LHH】 → とっても【LLHH】
すごく【LHL】 → すっごく【LLHL】 (The original accent should be すごく【HLL】, but I have never heard that)
すこし【LHL】 → すっこし【LLHL】
ひどい【LHL】 → ひっどい【LLHL】
さっき seem to be an colloquial from rather than an emphasized form.
たった is not always interchangeable with ただ
Some intonation may affect the vowel length.
You can lengthen the っ and ん part of above adverbs, or lengthen the vowel before it. (ん or the vowel before are both lengthened as nasal vowels, I think they don't make any difference.)
You can lengthen the second last syllable (last syllable of the stem) of a verb or an adjective.
Sometimes it may sound absentmindedly.
Auxiliary verbs like る/く/い/ぬ/ん are never lengthened. But た can.
Imperative forms lengthen the last syllable normally.
The last particle or the last syllable of a noun can be stressed and lengthened. I feel it sounds like the speaker want to make sure he is understood. The stressed syllable is always pronounced in high pitch.
The first syllable of a verb, adjective or adverb may be lengthened, to produce some exaggerated or dramatic effects.