Because of a phonological process know as compression, every can be said with either 2 or 3 syllables. This happens to coincide with the "written method" described (see full post below) which comes up with exactly that answer. There's no way round the two answer problem. Writing, of course, doesn't consist of sound and therefore doesn't have syllables, and this is part of the issue.
Well, all of these rules are problematic. To give an example, the chin one won't work at all if a consonant at the beginning of a syllable requires the mouth to be more open than the following vowel. This is what happens in the second syllable of the word sorry. Your chin's only going to hit your hand for the first syllable there, not the second (try it!). However, setting those many various issues aside, let's have a look at the interesting problem that the Original Poster is having with the word every.
Special features of Every:
There's a reason why the Original Poster is having a problem with every, in particular. As mentioned in the comments by @Peter Shor and @John Lawler, pronunciation varies between individuals, and also within the speech of any given single individual. So a given person might say the word every with either two or three syllables depending on many different factors, for example the number of unstressed syllables following the word, how fast they're speaking, who they're speaking to and why they're speaking in the first place. The reason this is possible is that the word every is liable to a phonetic and phonological process known as ᴄᴏᴍᴘʀᴇssɪᴏɴ.
English syllables come in two parts. There's the Onset and the Rhyme. The rhyme is obligatory, but the onset is an optional feature. The onset is usually a consonant or group of consonants at the beginning of the syllable, before the vowel. The rhyme is everything else. So in the word cat /kæt/, the onset is /k/ and the rhyme is /æt/.
Now the rhyme is further split into two parts. It has the most sonorous musical and vowellish part, the Nucleus, which is obligatory. It can also have a Coda, which involves the syllable getting both quieter and less sonorant. Codas are usually consonants or consonant clusters. So in /kæt/ the nucleus is /æ/ and the coda is /t/. The syllable itself represents a peak in sonority. If it has an onset and a coda, then these will represent the dips in sonority at either end of the syllable.
Notice that I said that nucleuses are usually vowels. This is because we can, in special circumstances, have a syllabic consonant. This is when the nucleus of a syllable is a consonant. For example, in the word criticism /krɪtɪsɪzm/, the last syllable just consists of an /m/ sound. The consonants /r, l/ and the nasals /m, n, ŋ/ also frequently occur as syllabic consonants in English.
Back to every. The most expanded pronunciation of the word every is this:
I've used the standard UK transcription here, as used by John Wells in the Longman Pronunciation Dictionary. You will see that the second vowel there is a schwa /ə/, a mid-central vowel which only ever occurs in unstressed syllables.
If we agree with Wells that, other things being equal, a consonant will usually be syllabified with a stressed syllable when between two vowels, then the /v/ in every belongs in the first, stressed syllable. In the pronunciation of every shown above, the second syllable has no onset and consists of just a rhyme with a schwa as its nucleus.
In English when a schwa is followed by an /l/ or /r/ or a nasal such as /m, n, ŋ/ there is usually an alternative possible pronunciation, which has no schwa, but instead uses the following consonant as a nucleus, in other words as a syllabic consonant. When transcribing the word, this can be shown by using a small diacritic under the consonant in question. With the word every this would look like this:
This pronunciation of every, like the one shown in (1) has three syllables, but this time the nucleus of the second syllable is the consonant /r/. This consonant will have a longer duration here than it would if occurring in an onset or a coda.
For most speakers, however, it is possible for a further reduction to take place and for the /r/ there to become the onset of the following syllable. In this case the /r/ will be quieter and significantly shorter in duration. This 'process' results in the loss of a syllable, of course. The resulting pronunciation is shown below:
In the second and last syllable here the /r/ is the onset and /i/ the nucleus.
This same type of variation can be seen in (4, 5) below:
- happening: hæpənɪŋ --> hæpn̩ɪŋ --> hæpnɪŋ
- pedalling: pedəlɪŋ --> pədl̩ɪŋ --> pedlɪŋ
This is one type of compression. There are others.
The Original Poster's Question
The Original Poster asks how many syllables every has according to the "Written Method." The answer here is easy: 2 or 3. If the person applying the rule arbitrarily decides that the pronunciation is /'evəri/, then they will decide that the second < e > in every has a sound and is not a silent letter. In this case every has three syllables according to the given rules. However, if they decide the pronunciation is /'evri/, then the second < e > in every is silent and they will therefore need to subtract 1 to find the number of syllables, giving them the answer 2. The reality is that writing doesn't have syllables (apart from those assigned in the mind of the reader).
I can hear some people saying "OK, but which pronunciation is the right one, the one with two syllables or the one with three? [Sigh. Whatever happened to free speech?!]
There is no correct pronunciation. The rules of English phonology allow for both. Native speakers use both. That's all there is to it. If you're looking to beat yourself with a riding crop for using the wrong one, go ahead, feel free. Make your choice and stick with it and administer your punishment accordingly. If you feel a deep need to apply your riding crop to others, however, please do ask first.