The following is courtesy of Rajita, whom the deva-s have given me the fortune to know. I have only worked [partially] on akShara-shuddhi of the mantra readings and put it together here with due permission.
The kaTha dIkShita-s who were shrauta ritualists as well as well accomplished tantrics had a distinctive pradoShaM rite on the trayodashi before mahAshivarAtrI and that is described here. Interestingly they observed fast on trayodashi during the day time. The rite involves the worship of baTuka bhairava, paramashiva, sadashiva and his parivAra.
First a copper kalasha is taken and filled with sugar syrup. Walnuts are soaked in it this syrup and the kalasha is capped with a coconut with mango leaves. The kalasha is installed in the maNDapa and surrounded by 64 haridra bimba-s which are the yoginIs. Then in front of them clay idols of shiva, umA, kumAra and gaNanAtha are placed.
First the vinAyaka is meditated up with :
shuklAmbhara-dharam devaM shashi-varnam chathur-bhujaM
prasanna vadanaM dhyAyet sarva-vighnopa-shanthaye ||
Then he is invoked into his clay idol with the formula:
gaM gaNapataye namaH |
Then the japa of his mantra is done:
OM shrIM hrIM klIM glauM gaM gaNapataye vara-varada sarva-janaM me vashamAnaya svAhA ||
Then a vinAyaka mudra is shown thus: the middle finger of the right hand is stretched out and slightly curved.
Then the bali of a rice ball is offered with the formula:
gAM gIM gUM gaM gaNapataye vara-varada sarva-janaM me vashamAnaya sarvopachAra sahitaM baliM gR^ihNa gR^ihNa svAhA ||
Then one invokes baTuka bhairva into the syrup pot with walnuts with the formula:
oM baM baTukAya namaH |
Then one meditates on him with fair complexion, with deep blue clothing, with two hands holding a trishUla and a skull with a yantra inscribed on it, with cobra garlands and surrounded by howling dogs.
baTuka bhairava mantra is used during this meditation:
hrIM baTukAya ApaduddhArana kuru kuru baTukAya hrIM ||
homa may next be offered to baTuka bhairava with this mantra.
Then the index finger and thumb and joined to show the baTuka mudra and then the following incantation is used to offer rice ball offerings:
ehyehi devI-putra baTukanAtha kapila jaTA bhAra bhAsura trinetra jvAlAmukha sarva-vighnAn nAshaya nAshaya sarvopachAra sahitaM baliM gR^ihNa gR^ihNa svAhA ||
Then the yoginIs are invoked into the biMba-s with the mantra: yAM yoginibhyo namaH ||
Then they are worshipped with the formula aiM hrIM shrIM ||
Then the yoginI mudra is shown: The middle finger, ring finger and thumbs are bent so that their tips meet to form a circle.
Then the yoginis are offered bali with the formula:
UrdhvaM brahmaNDato vA divi gaganatale bhUtale niSkale vA pAtAle vAtale vA .anale vA salila pavanayor yatra kutra sthitA vA kShetre pIThopapIThAdiShu cha kR^itapadA dhupa -dIpAdikena prItA devyaH sadA naH shubha-bali-vidhinA pAntu vIrendra -vandyAH | yAM yoginIbhyaH svAhA ||
Then one meditates on paramshiva using the dhyAna:
nAnA-kalpAbhirAmApaghanam-abhi-matArtha-pradaM suprasannaM |
padaMasthaM pa~nchavaktraM sphaTika-maNi-nibhaM pArvatIshaM namAmI ||
The he meditates on the mantra: aiM hrIM shrIM hasakhaphreM hasauH || or hauM ||
This is then the worship of sadAshiva and his clan is done.
One mediates on sadAshiva thus:
bibhrad dorbiH kuTAraM mR^igaM abhaya-varau suprasanno maheshaH sarvAla~NkAra-dIptaH sarasija-nilayo vyAghra-charmAttvAsAH |
dhyeyo muktAparAgAmR^ita-rasa-kalitAdri-prabhaH pa~nchavaktras-tryAkShaH koTIrakoTI-ghaTita-tuhina-rochiH kalottu~Nga-mauliH ||
sadyo vedAkShamAlA .abhaya-varadakaraH kunda-mandAra-gauro vAmaH kAshmIra-varNo .abhaya varada parashva .akShamAlA-vilAsI |
akSha-srag-veda-pAshA-.a~Nkusha-Damaruka-khaTvA~Nga-shUlAn kapAlaM bibhrANo bhIMa-daMSTro .a~njana-ruchira-tanur-bhItidashchA .apyaghoraH ||
vidyud-varNA .atha vedA .abhaya-varada kuThArAn dadhat pUruShAkhyaH proktAH sarve trinetrA vidhR^itamukha-chatuShkAsh-chatur-bAhavashcha |
muktA-gauro .abhayeShTAdhika-kara-kamalo .aghorataH pa~nchavaktras-tvIsho dhyeyo .ambujanmodbhava-muraripu-rudreshvarAH syuH shivAntAH ||
One then praises shiva saying:
vishva-grAsAya vilasat-kAla-kUTa-viShAshine |
tat-kala~NkA~Nkita-grIva-nIlakaNThAya te namaH |
daMShTrA-karAlaM divi nR^ityamAnaM hutAsha-vaktraM jvalanArka-rUpaM |
sahasra-pAdAkShi-shirobhi yuktaM bhavantam-ekaM praNamAmi rudraM ||
namo.astu somAya su-madhyamAya namo.astu devAya hiraNya-bAho |
namo.agni-chandrArka-vilochanAya namo.ambikAyAH pataye mR^iDAya ||
Then he is invoked with the five fold mantras.
Then there is recitation of the kaTha rudrIya, which begins with “tat-puruShAya vidhmahe…”
It is concluded with the oblation:
tasmai te deva bhavAya sharvAya pashupataya ugrAya devAya mahate devAya rudrAyeshAnAyAshanaye svAhA ||
evidently from the kaTHa oral tradition (compare with similar taittirIya mantra).
Then umA is worshipped with the formula:
hrIM namo brahma shrI-rAjite rAja pUjite jaya vijaye gaurI gANdhArI tribhuvana-vashaMkarI sarva loka-vashaMkarI su su du du ghe ghe vA vA hrIM svAhA ||
Then skanda is invoked with the formula: ShaM ShANmukhAya namaH ||
He his worshiped with the mantra: OM kaM kShaM kaM kArtikeyAya phaT ||
Finally kShetrapAla is worshiped an offered bali.
Then the soaked walnuts are offered as prasAda to break the fast.